Question

complete the statements.
the congruent - complements theorem implies that if m∠agf is 60°, m∠cgh is 00°
the vertical - angles theorem implies that if m∠igd is 20°, m∠cdh 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. If \(\angle AGF\) and \(\angle CGH\) are complementary to the same angle (in this case, the right - angle at \(G\)), and \(m\angle AGF = 60^{\circ}\), then since they are congruent, \(m\angle CGH=m\angle AGF\).

Step2: Determine the measure of \(\angle CGH\)

\(m\angle CGH = 60^{\circ}\)

Step3: Recall vertical - angles theorem

The vertical - angles theorem states that vertical angles are congruent. \(\angle IGD\) and \(\angle CGH\) are vertical angles. If \(m\angle IGD = 20^{\circ}\), then since vertical angles are congruent, \(m\angle CGH=m\angle IGD\)

Answer:

60; 20