Question

In the diagram, $\overline{\text{AB}}\perp \overline{\text{BC}}$.

Name:

a. two supplementary angles.

b. two complementary angles.

Short answer

a. Two supplementary angles are∠3 and∠4.

b. Two complementary angles are∠1 and∠2.

Step-by-step solution

Part a. Step 1. Observe the diagram.

Here, $\overline{AB}\perp \overline{BC}$.

Part a. Step 2. Show the calculation.

As $\overline{AB}\perp \overline{BC}$and

From the figure,

$m\angle 3+m\angle 4=180°$.

Two angles whose sum is 180° are called supplementary angles.

So, ∠3 and ∠4 are two supplementary angles.

Part a. Step 3. State the conclusion.

Therefore, the two supplementary angles are ∠3 and ∠4.

Part b. Step 1. Observe the diagram.

Here,$\overline{AB}\perp \overline{BC}$.

Part b. Step 2. Show the calculation.

As $\overline{AB}\perp \overline{BC}$and

From the figure,

$m\angle 1+m\angle 2=90°$

Two angles whose sum is 90° are called complementary angles

So, ∠1 and ∠2 are two complementary angles.

Part b. Step 3. State the conclusion.

Therefore, the two complementary angles are ∠1 and ∠2.