You are told that the two angles are supplementary. That means that when you add the measure of angle A (call it mA) and the measure of angle B (call it mB) the resulting sum is 180 degrees. This relationship can be written in equation form as: . mA + mB = 180 . You are also told that the two angles are congruent. This means that their measures are equal. You can write this relationship as the equation: . mA = mB . From this second equation you can see that wherever you have mA you can substitute mB in its place because they are equals. So go back to the equation: . mA + mB = 180 .
In place of mA substitute mB. This makes the equation become: . mB + mB = 180 . On the left side you can see that the sum is 2 times mB or 2*mB. Make this simplification to get: . 2*mB = 180 . To solve for mB divide both sides of this equation by 2. When you do that division the equation reduces to: . mB = 180/2 = 90 . This tells you that the measure of angle B is 90 degrees, and that means that the measure of angle A is also equal to 90 degrees because the two angles are congruent.
