Page 1 Q u e s t i o n : 8 6 One angle is equal to three times its supplement. The measure of the angle is a 130° b 135° c 90° d 120° S o l u t i o n : Let the supplement of the angle be Therefore, according to the given statement, the required angle measures Since the angles are supplementary, therefore their sum must be equal to Or we can say that Thus, the supplement of angle measures Hence, the correct choice is b . Q u e s t i o n : 8 7 Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD = i 86° Page 2 Q u e s t i o n : 8 6 One angle is equal to three times its supplement. The measure of the angle is a 130° b 135° c 90° d 120° S o l u t i o n : Let the supplement of the angle be Therefore, according to the given statement, the required angle measures Since the angles are supplementary, therefore their sum must be equal to Or we can say that Thus, the supplement of angle measures Hence, the correct choice is b . Q u e s t i o n : 8 7 Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD = i 86° ii 90° iii 94° iv 137° S o l u t i o n : Let us draw the following diagram showing two lines and intersecting at a point . Thus, ?AOD, ?AOC, ?COB and ?BOD form a complete angle, that is the sum of these four angle is . That is, ?AOD + ?AOC + ?COB + ?BOD = 360° ... i It is given that ...ii Subtracting ii from i , we get: Hence, the correct choice is a . Q u e s t i o n : 8 8 Two straight lines AB and CD cut each other at O. If ?BOD = 63°, then ?BOC = a 63° b 117° c 17° d 153° S o l u t i o n : Let us draw the following diagram showing two lines and intersecting each other at a point . Page 3 Q u e s t i o n : 8 6 One angle is equal to three times its supplement. The measure of the angle is a 130° b 135° c 90° d 120° S o l u t i o n : Let the supplement of the angle be Therefore, according to the given statement, the required angle measures Since the angles are supplementary, therefore their sum must be equal to Or we can say that Thus, the supplement of angle measures Hence, the correct choice is b . Q u e s t i o n : 8 7 Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD = i 86° ii 90° iii 94° iv 137° S o l u t i o n : Let us draw the following diagram showing two lines and intersecting at a point . Thus, ?AOD, ?AOC, ?COB and ?BOD form a complete angle, that is the sum of these four angle is . That is, ?AOD + ?AOC + ?COB + ?BOD = 360° ... i It is given that ...ii Subtracting ii from i , we get: Hence, the correct choice is a . Q u e s t i o n : 8 8 Two straight lines AB and CD cut each other at O. If ?BOD = 63°, then ?BOC = a 63° b 117° c 17° d 153° S o l u t i o n : Let us draw the following diagram showing two lines and intersecting each other at a point . Let the required angle measures . Also, and form a linear pair. Therefore, their sum must be equal to . That is, It is given that . Substituting, this value above, we get: Hence, the correct choice is b . Q u e s t i o n : 8 9 Consider the following statements: When two straight lines intersect: i adjacent angles are complementary ii adjacent angles are supplementary iii opposite angles are equal iv opposite angles are supplementary Of these statements a i and ii are correct b ii and iii are correct c i and iv are correct d ii and iv are correct S o l u t i o n : Page 4 Q u e s t i o n : 8 6 One angle is equal to three times its supplement. The measure of the angle is a 130° b 135° c 90° d 120° S o l u t i o n : Let the supplement of the angle be Therefore, according to the given statement, the required angle measures Since the angles are supplementary, therefore their sum must be equal to Or we can say that Thus, the supplement of angle measures Hence, the correct choice is b . Q u e s t i o n : 8 7 Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD = i 86° ii 90° iii 94° iv 137° S o l u t i o n : Let us draw the following diagram showing two lines and intersecting at a point . Thus, ?AOD, ?AOC, ?COB and ?BOD form a complete angle, that is the sum of these four angle is . That is, ?AOD + ?AOC + ?COB + ?BOD = 360° ... i It is given that ...ii Subtracting ii from i , we get: Hence, the correct choice is a . Q u e s t i o n : 8 8 Two straight lines AB and CD cut each other at O. If ?BOD = 63°, then ?BOC = a 63° b 117° c 17° d 153° S o l u t i o n : Let us draw the following diagram showing two lines and intersecting each other at a point . Let the required angle measures . Also, and form a linear pair. Therefore, their sum must be equal to . That is, It is given that . Substituting, this value above, we get: Hence, the correct choice is b . Q u e s t i o n : 8 9 Consider the following statements: When two straight lines intersect: i adjacent angles are complementary ii adjacent angles are supplementary iii opposite angles are equal iv opposite angles are supplementary Of these statements a i and ii are correct b ii and iii are correct c i and iv are correct d ii and iv are correct S o l u t i o n : Let us draw the following diagram showing two straight lines AD and BC intersecting each other at a point . Now, let us consider each statement one by one: i When two lines intersect adjacent angles are complementary. This statement is incorrect Explanation: As the adjacent angles form a linear pair and they are supplementary. ii When two lines intersect adjacent angles are supplementary. This statement is correct. Explanation: As the adjacent angles form a linear pair and they are supplementary. iii When two lines intersect opposite angles are equal. This statement is correct. Explanation: As the vertically opposite angles are equal. iv When two lines intersect opposite angles are supplementary. This statement is incorrect. Explanation: As the vertically opposite angles are equal Thus, out of all, ii and iii are correct. Hence, the correct choice is b . Q u e s t i o n : 9 0 Given ?POR = 3x and ?QOR = 2x + 10°. If POQ is a straight line, then the value of x is a 30° b 34° c 36° Page 5 Q u e s t i o n : 8 6 One angle is equal to three times its supplement. The measure of the angle is a 130° b 135° c 90° d 120° S o l u t i o n : Let the supplement of the angle be Therefore, according to the given statement, the required angle measures Since the angles are supplementary, therefore their sum must be equal to Or we can say that Thus, the supplement of angle measures Hence, the correct choice is b . Q u e s t i o n : 8 7 Two straight line AB and CD intersect one another at the point O. If ?AOC + ?COB + ?BOD = 274°, then ?AOD = i 86° ii 90° iii 94° iv 137° S o l u t i o n : Let us draw the following diagram showing two lines and intersecting at a point . Thus, ?AOD, ?AOC, ?COB and ?BOD form a complete angle, that is the sum of these four angle is . That is, ?AOD + ?AOC + ?COB + ?BOD = 360° ... i It is given that ...ii Subtracting ii from i , we get: Hence, the correct choice is a . Q u e s t i o n : 8 8 Two straight lines AB and CD cut each other at O. If ?BOD = 63°, then ?BOC = a 63° b 117° c 17° d 153° S o l u t i o n : Let us draw the following diagram showing two lines and intersecting each other at a point . Let the required angle measures . Also, and form a linear pair. Therefore, their sum must be equal to . That is, It is given that . Substituting, this value above, we get: Hence, the correct choice is b . Q u e s t i o n : 8 9 Consider the following statements: When two straight lines intersect: i adjacent angles are complementary ii adjacent angles are supplementary iii opposite angles are equal iv opposite angles are supplementary Of these statements a i and ii are correct b ii and iii are correct c i and iv are correct d ii and iv are correct S o l u t i o n : Let us draw the following diagram showing two straight lines AD and BC intersecting each other at a point . Now, let us consider each statement one by one: i When two lines intersect adjacent angles are complementary. This statement is incorrect Explanation: As the adjacent angles form a linear pair and they are supplementary. ii When two lines intersect adjacent angles are supplementary. This statement is correct. Explanation: As the adjacent angles form a linear pair and they are supplementary. iii When two lines intersect opposite angles are equal. This statement is correct. Explanation: As the vertically opposite angles are equal. iv When two lines intersect opposite angles are supplementary. This statement is incorrect. Explanation: As the vertically opposite angles are equal Thus, out of all, ii and iii are correct. Hence, the correct choice is b . Q u e s t i o n : 9 0 Given ?POR = 3x and ?QOR = 2x + 10°. If POQ is a straight line, then the value of x is a 30° b 34° c 36° d none of these S o l u t i o n : Let us draw the following figure, showing as a straight line. Thus, and form a linear pair, therefore their sum must be supplementary. That is; It is given that and On substituting these two values above, we get: Hence, the correct choice is b . Q u e s t i o n : 9 1 In the given figure, AOB is a straight line. If ?AOC + ?BOD = 85°, then ?COD = a 85° b 90° c 95° d 100° S o l u t i o n : It is given that is a straight line.Read More

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