The sum of all angles must equal 180°. Since you already have two angles for the larger triangle, all you need to do to find m < x is by subtracting m < 63° and m < 36° from 180°:
m < x = 180° - m < 63° - m < 36°
m < x = 81°
Therefore, < x = 81°
For the smaller triangle (acute), what you could do to find m < z is by subtracting m < x from 180°. We can do it that way because < x and < z are supplementary angles whose sum add up to 180°.
m < z = 180° - m < x
m < z = 180° - m < 81°
m < z = 99°
Therefore, < z = 99°
Lastly, to find m < y, subtract m < 13°and m < z° from 180°:
m < y = 180° - m < z° - m < 13°
m < y = 180° - m< 99° - m< 13°
m < y = 68°
Therefore, the measure of the following angles are:
< x = 81°
< y = 68°
< z = 99°
