Page 1 Q u e s t i o n : 7 4 Define complementary angles. S o l u t i o n : Complementary Angles: Two angles, the sum of whose measures is , are called complementary angles. Thus, angles and are complementary angles, if Example 1: Angles of measure and are complementary angles, because Example 2: Angles of measure and are complementary angles, because Q u e s t i o n : 7 5 Define supplementary angles. S o l u t i o n : Supplementary Angles: Two angles, the sum of whose measures is , are called supplementary angles. Thus, angles and are supplementary angles, if Example 1: Angles of measure and are supplementary angles, because Example 2: Angles of measure and are supplementary angles, because Page 2 Q u e s t i o n : 7 4 Define complementary angles. S o l u t i o n : Complementary Angles: Two angles, the sum of whose measures is , are called complementary angles. Thus, angles and are complementary angles, if Example 1: Angles of measure and are complementary angles, because Example 2: Angles of measure and are complementary angles, because Q u e s t i o n : 7 5 Define supplementary angles. S o l u t i o n : Supplementary Angles: Two angles, the sum of whose measures is , are called supplementary angles. Thus, angles and are supplementary angles, if Example 1: Angles of measure and are supplementary angles, because Example 2: Angles of measure and are supplementary angles, because Q u e s t i o n : 7 6 Define adjacent angles. S o l u t i o n : Adjacent angles: Two angles are called adjacent angles, if: i. They have the same vertex, ii. They have a common arm, and iii. Uncommon arms are on either side of the common arm. In the figure above, and have a common vertex . Also, they have a common arm and the distinct arms and , lies on the opposite sides of the line . Therefore, and are adjacent angles. Q u e s t i o n : 7 7 The complement of an acute angle is .............. S o l u t i o n : The complement of an acute angle is an acute angle. Explanation: As the sum of the complementary angles is . Let one of the angle measures . Then, other angle becomes , which is clearly an acute angle. Q u e s t i o n : 7 8 The supplement of an acute angle is ................. S o l u t i o n : The supplement of an acute angle is an obtuse angle. Explanation: As the sum of the supplementary angles is . Let one of the angle measures , such that Let the other angle measures As the angles are supplementary there sum is . Then, other angle y is clearly an obtuse angle. Illustration: Let the given acute angle be Page 3 Q u e s t i o n : 7 4 Define complementary angles. S o l u t i o n : Complementary Angles: Two angles, the sum of whose measures is , are called complementary angles. Thus, angles and are complementary angles, if Example 1: Angles of measure and are complementary angles, because Example 2: Angles of measure and are complementary angles, because Q u e s t i o n : 7 5 Define supplementary angles. S o l u t i o n : Supplementary Angles: Two angles, the sum of whose measures is , are called supplementary angles. Thus, angles and are supplementary angles, if Example 1: Angles of measure and are supplementary angles, because Example 2: Angles of measure and are supplementary angles, because Q u e s t i o n : 7 6 Define adjacent angles. S o l u t i o n : Adjacent angles: Two angles are called adjacent angles, if: i. They have the same vertex, ii. They have a common arm, and iii. Uncommon arms are on either side of the common arm. In the figure above, and have a common vertex . Also, they have a common arm and the distinct arms and , lies on the opposite sides of the line . Therefore, and are adjacent angles. Q u e s t i o n : 7 7 The complement of an acute angle is .............. S o l u t i o n : The complement of an acute angle is an acute angle. Explanation: As the sum of the complementary angles is . Let one of the angle measures . Then, other angle becomes , which is clearly an acute angle. Q u e s t i o n : 7 8 The supplement of an acute angle is ................. S o l u t i o n : The supplement of an acute angle is an obtuse angle. Explanation: As the sum of the supplementary angles is . Let one of the angle measures , such that Let the other angle measures As the angles are supplementary there sum is . Then, other angle y is clearly an obtuse angle. Illustration: Let the given acute angle be Then, the other angle becomes This is clearly an obtuse angle. Q u e s t i o n : 7 9 The supplement of a right angle is .............. S o l u t i o n : We have to find the supplement of a right angle. We know that a right angle is equal to . Let the required angle be . Since the two angles are supplementary, therefore their sum must be equal to . Thus, the require angle becomes Q u e s t i o n : 8 0 Write the complement of an angle of measure x°. S o l u t i o n : We have to write the complement of an angle which measures . Let the other angle be . We know that the sum of the complementary angles be 90°. Therefore, Q u e s t i o n : 8 1 Write the supplement of an angle of measure 2y°. S o l u t i o n : Let the required angle measures It is given that two angles measuring and are supplementary. Therefore, their sum must be equal to . Or, we can say that: Hence, the required angle measures . Q u e s t i o n : 8 2 If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes. S o l u t i o n : It is given that the six spokes are equally spaced, thus, two adjacent spokes subtend equal angle at the centre of the wheel. Let that angle measures Also, the six spokes form a complete angle, that is, Page 4 Q u e s t i o n : 7 4 Define complementary angles. S o l u t i o n : Complementary Angles: Two angles, the sum of whose measures is , are called complementary angles. Thus, angles and are complementary angles, if Example 1: Angles of measure and are complementary angles, because Example 2: Angles of measure and are complementary angles, because Q u e s t i o n : 7 5 Define supplementary angles. S o l u t i o n : Supplementary Angles: Two angles, the sum of whose measures is , are called supplementary angles. Thus, angles and are supplementary angles, if Example 1: Angles of measure and are supplementary angles, because Example 2: Angles of measure and are supplementary angles, because Q u e s t i o n : 7 6 Define adjacent angles. S o l u t i o n : Adjacent angles: Two angles are called adjacent angles, if: i. They have the same vertex, ii. They have a common arm, and iii. Uncommon arms are on either side of the common arm. In the figure above, and have a common vertex . Also, they have a common arm and the distinct arms and , lies on the opposite sides of the line . Therefore, and are adjacent angles. Q u e s t i o n : 7 7 The complement of an acute angle is .............. S o l u t i o n : The complement of an acute angle is an acute angle. Explanation: As the sum of the complementary angles is . Let one of the angle measures . Then, other angle becomes , which is clearly an acute angle. Q u e s t i o n : 7 8 The supplement of an acute angle is ................. S o l u t i o n : The supplement of an acute angle is an obtuse angle. Explanation: As the sum of the supplementary angles is . Let one of the angle measures , such that Let the other angle measures As the angles are supplementary there sum is . Then, other angle y is clearly an obtuse angle. Illustration: Let the given acute angle be Then, the other angle becomes This is clearly an obtuse angle. Q u e s t i o n : 7 9 The supplement of a right angle is .............. S o l u t i o n : We have to find the supplement of a right angle. We know that a right angle is equal to . Let the required angle be . Since the two angles are supplementary, therefore their sum must be equal to . Thus, the require angle becomes Q u e s t i o n : 8 0 Write the complement of an angle of measure x°. S o l u t i o n : We have to write the complement of an angle which measures . Let the other angle be . We know that the sum of the complementary angles be 90°. Therefore, Q u e s t i o n : 8 1 Write the supplement of an angle of measure 2y°. S o l u t i o n : Let the required angle measures It is given that two angles measuring and are supplementary. Therefore, their sum must be equal to . Or, we can say that: Hence, the required angle measures . Q u e s t i o n : 8 2 If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes. S o l u t i o n : It is given that the six spokes are equally spaced, thus, two adjacent spokes subtend equal angle at the centre of the wheel. Let that angle measures Also, the six spokes form a complete angle, that is, Therefore, Hence, the measure of the angle between two adjacent spokes measures . Q u e s t i o n : 8 3 An angle is equal to its supplement. Determine its measure. S o l u t i o n : Let the supplement of the angle be According the given statement, the required angle is equal to its supplement, therefore, the required angle becomes . Sine both the angles are supplementary, therefore, their sum must be equal to Or we can say that: Hence, the required angle measures . Q u e s t i o n : 8 4 An angle is equal to five times its complement. Determine its measure. S o l u t i o n : Let the complement of the required angle measures Therefore, the required angle becomes Since, the angles are complementary, thus, their sum must be equal to . Or we can say that : Hence, the required angle becomes: Q u e s t i o n : 8 5 How many pairs of adjacent angles are formed when two lines intersect in a point? S o l u t i o n : Let us draw the following diagram showing two lines and intersecting at a point . Page 5 Q u e s t i o n : 7 4 Define complementary angles. S o l u t i o n : Complementary Angles: Two angles, the sum of whose measures is , are called complementary angles. Thus, angles and are complementary angles, if Example 1: Angles of measure and are complementary angles, because Example 2: Angles of measure and are complementary angles, because Q u e s t i o n : 7 5 Define supplementary angles. S o l u t i o n : Supplementary Angles: Two angles, the sum of whose measures is , are called supplementary angles. Thus, angles and are supplementary angles, if Example 1: Angles of measure and are supplementary angles, because Example 2: Angles of measure and are supplementary angles, because Q u e s t i o n : 7 6 Define adjacent angles. S o l u t i o n : Adjacent angles: Two angles are called adjacent angles, if: i. They have the same vertex, ii. They have a common arm, and iii. Uncommon arms are on either side of the common arm. In the figure above, and have a common vertex . Also, they have a common arm and the distinct arms and , lies on the opposite sides of the line . Therefore, and are adjacent angles. Q u e s t i o n : 7 7 The complement of an acute angle is .............. S o l u t i o n : The complement of an acute angle is an acute angle. Explanation: As the sum of the complementary angles is . Let one of the angle measures . Then, other angle becomes , which is clearly an acute angle. Q u e s t i o n : 7 8 The supplement of an acute angle is ................. S o l u t i o n : The supplement of an acute angle is an obtuse angle. Explanation: As the sum of the supplementary angles is . Let one of the angle measures , such that Let the other angle measures As the angles are supplementary there sum is . Then, other angle y is clearly an obtuse angle. Illustration: Let the given acute angle be Then, the other angle becomes This is clearly an obtuse angle. Q u e s t i o n : 7 9 The supplement of a right angle is .............. S o l u t i o n : We have to find the supplement of a right angle. We know that a right angle is equal to . Let the required angle be . Since the two angles are supplementary, therefore their sum must be equal to . Thus, the require angle becomes Q u e s t i o n : 8 0 Write the complement of an angle of measure x°. S o l u t i o n : We have to write the complement of an angle which measures . Let the other angle be . We know that the sum of the complementary angles be 90°. Therefore, Q u e s t i o n : 8 1 Write the supplement of an angle of measure 2y°. S o l u t i o n : Let the required angle measures It is given that two angles measuring and are supplementary. Therefore, their sum must be equal to . Or, we can say that: Hence, the required angle measures . Q u e s t i o n : 8 2 If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes. S o l u t i o n : It is given that the six spokes are equally spaced, thus, two adjacent spokes subtend equal angle at the centre of the wheel. Let that angle measures Also, the six spokes form a complete angle, that is, Therefore, Hence, the measure of the angle between two adjacent spokes measures . Q u e s t i o n : 8 3 An angle is equal to its supplement. Determine its measure. S o l u t i o n : Let the supplement of the angle be According the given statement, the required angle is equal to its supplement, therefore, the required angle becomes . Sine both the angles are supplementary, therefore, their sum must be equal to Or we can say that: Hence, the required angle measures . Q u e s t i o n : 8 4 An angle is equal to five times its complement. Determine its measure. S o l u t i o n : Let the complement of the required angle measures Therefore, the required angle becomes Since, the angles are complementary, thus, their sum must be equal to . Or we can say that : Hence, the required angle becomes: Q u e s t i o n : 8 5 How many pairs of adjacent angles are formed when two lines intersect in a point? S o l u t i o n : Let us draw the following diagram showing two lines and intersecting at a point . We have the following pair of adjacent angles, so formed: and and and and Hence, in total four pair of adjacent angles are formed.Read More

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