angles that are congruent and supplementary must be
right angles
To determine the property that angles must possess in order to be both congruent and supplementary, we need to understand the definitions of congruence and supplementarity.
1. Congruent angles: When two angles are congruent, it means they have the same measure. In other words, their angles are equal.
2. Supplementary angles: Two angles are considered supplementary if their measures add up to 180 degrees. In other words, when you sum the measures of two supplementary angles, the result is 180 degrees.
Now, to find angles that are both congruent and supplementary, we need to set up an equation based on the above definitions.
Let's denote the measures of the two angles as x. Since the angles are congruent, their measures are equal, meaning that x = x. Additionally, since the angles are supplementary, their measures sum up to 180 degrees, which can be expressed as x + x = 180.
Simplifying the equation, we have:
2x = 180
To isolate x, we divide both sides of the equation by 2:
2x/2 = 180/2
x = 90
Therefore, the only possible solution is x = 90. This means that the angles must both have a measure of 90 degrees in order to be congruent and supplementary.