The Supplements of Congruent Angles: A Concept in Angle Measures and Their Congruency

supplements of congruent angles are congruent

The statement “supplements of congruent angles are congruent” relates to the concept of angle measures and their supplements

The statement “supplements of congruent angles are congruent” relates to the concept of angle measures and their supplements.

An angle and its supplement are two angles whose measures add up to 180 degrees. If two angles are congruent, it means that they have the same measure.

Let’s consider two congruent angles, angle A and angle B. Since they are congruent, we can denote their measures as:

Measure of angle A = x
Measure of angle B = x

The supplement of angle A would be an angle that, when added to angle A, gives 180 degrees. Similarly, the supplement of angle B would be an angle that, when added to angle B, also gives 180 degrees.

So, to find the measures of the supplements of angle A and angle B, we can use the equation:

Measure of angle A + Measure of supplement of angle A = 180 degrees

Substituting the values of angle A and its supplement:

x + Measure of supplement of angle A = 180 degrees

Now, let’s look at angle B and its supplement:

Measure of angle B + Measure of supplement of angle B = 180 degrees

Substituting the values of angle B and its supplement:

x + Measure of supplement of angle B = 180 degrees

From these two equations, we can see that the measure of the supplement of angle A is equal to the measure of the supplement of angle B. This is because the measures of angle A and angle B are congruent.

Therefore, we can conclude that the supplements of congruent angles are congruent.

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