Question

In the diagram below find the measure of each of the three angles and then state which two are complementary and which two are a supplementary pair. Answer question 1 and two.

Answer 1

1) ∠C and ∠G are supplementary while ∠A and ∠G are complementary.

2) Yes, ∠D is supplementary to ∠GAH

This is based on understanding complementary and supplementary angles.

By definition, complementary angles are two angles whose sum is equal to 90°. Meanwhile supplementary angles are those whose sum is equal to 180°.

• 1) From the angles drawn, we can see that ∠A and ∠G are less than 90° while ∠C is greater than 90° but less than 180°.

From inspection, ∠A looks same angle with ∠G. But, for them to be complementary they have to add up to 90°. Thus;

∠A + ∠G = 90°

Since ∠A = ∠G, then ∠A = ∠G = 90/2 = 45°

Now, ∠C appears to be the remaining part of ∠G to complete a straight line.

We know that sum of angles on a straight line is 180°

Thus;

∠C + ∠G = 180°

∠C + 45° = 180°

∠C = 180° - 45°

∠C = 135°

Thus, ∠C and ∠G are supplementary while ∠A and ∠G are complementary.

• 2) We see that  ∠D = 63°

For ∠D to be supplementary to ∠GAH, it means that ∠GAH must be 180° - 63° = 117°

By inspection, it looks permissible.

Thus, ∠D is supplementary to ∠GAH

Read more at; brainly.com/question/4853862