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If two adjacent angles are supplementary, then they form _________ .
- a)a linear pair of angles
- b)vertically opposite angles
- c)Corresponding angles
- d)a ray
Correct answer is 'A'. Can you explain this answer?
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If two adjacent angles are supplementary, then they form _________ .a)...
A linear pair is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then they are supplementary.
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If two adjacent angles are supplementary, then they form _________ .a)...
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If two adjacent angles are supplementary, then they form _________ .a)...
Supplementary Angles:
Supplementary angles are two angles that add up to 180 degrees. In other words, if the measures of two angles add up to 180 degrees, then they are supplementary angles.
Adjacent Angles:
Adjacent angles are two angles that share a common vertex and a common side but do not overlap. In other words, they are angles that are next to each other and have a common endpoint and a common side.
Linear Pair of Angles:
A linear pair of angles is formed when two adjacent angles are supplementary. In other words, if two adjacent angles add up to 180 degrees, they form a linear pair of angles.
Explanation:
When two adjacent angles are supplementary, it means that their measures add up to 180 degrees. This condition satisfies the definition of a linear pair of angles.
When two angles form a linear pair, they are always adjacent angles because they share a common vertex and a common side. Additionally, they are always supplementary because their measures add up to 180 degrees.
Therefore, if two adjacent angles are supplementary, it is always true that they form a linear pair of angles. Option A, "a linear pair of angles," is the correct answer to the question.
Example:
For example, let's consider two adjacent angles, angle A and angle B. If angle A measures 70 degrees, then angle B must measure 110 degrees in order for the two angles to be supplementary (70 + 110 = 180).
In this case, angle A and angle B form a linear pair of angles because they are adjacent (they share a common vertex and a common side) and their measures add up to 180 degrees.
Supplementary angles are two angles that add up to 180 degrees. In other words, if the measures of two angles add up to 180 degrees, then they are supplementary angles.
Adjacent Angles:
Adjacent angles are two angles that share a common vertex and a common side but do not overlap. In other words, they are angles that are next to each other and have a common endpoint and a common side.
Linear Pair of Angles:
A linear pair of angles is formed when two adjacent angles are supplementary. In other words, if two adjacent angles add up to 180 degrees, they form a linear pair of angles.
Explanation:
When two adjacent angles are supplementary, it means that their measures add up to 180 degrees. This condition satisfies the definition of a linear pair of angles.
When two angles form a linear pair, they are always adjacent angles because they share a common vertex and a common side. Additionally, they are always supplementary because their measures add up to 180 degrees.
Therefore, if two adjacent angles are supplementary, it is always true that they form a linear pair of angles. Option A, "a linear pair of angles," is the correct answer to the question.
Example:
For example, let's consider two adjacent angles, angle A and angle B. If angle A measures 70 degrees, then angle B must measure 110 degrees in order for the two angles to be supplementary (70 + 110 = 180).
In this case, angle A and angle B form a linear pair of angles because they are adjacent (they share a common vertex and a common side) and their measures add up to 180 degrees.
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If two adjacent angles are supplementary, then they form _________ .a)a linear pair of anglesb)vertically opposite anglesc)Corresponding anglesd)a rayCorrect answer is 'A'. Can you explain this answer?
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