13. Equal supplementary angles.
Answers
Answer:
two angle are called supplementary when their measure add up to 180 degrees
Step-by-step explanation:
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Equal supplementary angles are supplementary angles having same measure , that is 90° + 90° = 180°
In Maths, the meaning of supplementary is related to angles that make a straight angle together. It means, two angles are said to be supplementary angles when they add up to 180 degrees. Two angles are supplementary, if
One of its angles is an acute angle and another angle is an obtuse angle.Both of the angles are right angles.
This means that ∠A + ∠B = 180°.
See the figure below for a better understanding of the pair of angles that are supplementary.
Properties
The important properties of supplementary angles are:
The two angles are said to be supplementary angles when they add up to 180°.The two angles together make a straight line, but the angles need not be together.“S” of supplementary angles stands for the “Straight” line. This means they form 180°.
How to Find Supplementary Angles?
For example, if you had given that two angles form supplementary angles and you are provided with one angle and then asked to find the other angle, you can easily find the other angle using the formula.
∠A = 180° – ∠B (or)
∠B = 180° – ∠A
Adjacent and Non-Adjacent Supplementary Angles
The supplementary angles may be classified as either adjacent or non-adjacent. The adjacent supplementary angles share the common line segment or arm with each other, whereas the non-adjacent supplementary angles do not share the line segment or arm.
Supplementary Angles Theorem
The supplementary angle theorem states that if two angles are supplementary to the same angle, then the two angles are said to be congruent.
Proof:
If ∠x and ∠y are two different angles that are supplementary to a third angle ∠z, such that,
∠x + ∠z = 180 ……. (1)
∠y + ∠z = 180 ……. (2)
Then, from the above two equations we can say,
∠x = ∠y
Hence proved.
Examples
Some of the examples of supplementary angles are:
120° + 60° = 180°
90° + 90° = 180°
140° + 40° = 180°
96° + 84° = 180°
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