Question

figure is shown. y 10 9 8 7 6 5 4 3 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 complete the statements. the congruent complements theorem implies that if m∠agf is 60°, m∠cgh is the vertical angles theorem implies that if m∠igd is m∠cgh is 20°.

Explanation:

Step1: Recall congruent - complements theorem

The congruent - complements theorem states that if two angles are complementary to the same angle, then they are congruent. $\angle AGF$ and $\angle CGH$ are complementary to $\angle FGC$. Since $\angle AGB = 90^{\circ}$, if $m\angle AGF=60^{\circ}$, then $m\angle FGC = 90^{\circ}-m\angle AGF$. Also, $\angle FGC+\angle CGH = 90^{\circ}$. So, $m\angle CGH=m\angle AGF = 60^{\circ}$.

Step2: Recall vertical - angles theorem

Vertical angles are congruent. $\angle IGD$ and $\angle CGH$ are vertical angles. If $m\angle IGD = 20^{\circ}$, then by the vertical - angles theorem, $m\angle CGH = 20^{\circ}$.

Answer:

$60^{\circ}$; $20^{\circ}$