Question

Name two adjacent complementary angles.

Short answer

The two adjacent complementary angles are $\angle MPL$and $\angle QPL$.

Step-by-step solution

Step 1. Definition of adjacent angles and complementary angles.

The adjacent angles are the angles that have the common vertex and common side.

The complementary angles are the angles whose sum is $90°$.

Step 2. Observe the diagram.

From the given diagram it can be concluded that:

$\angle MPL=50$and $\angle QPL=40$.

The angles $\angle MPL$and $\angle QPL$are adjacent angles because they are having a common side and the common vertex P.

Step 3. Find the sum of the angles ∠MPL and ∠QPL.

The sum of the angles $\angle MPL$and $\angle QPL$is $\angle MPL+\angle QPL$.

Therefore,

$\angle MPL+\angle QPL=50+40$

$=90$

Therefore, the sum of the angles $\angle MPL$and $\angle QPL$is 90.

Therefore, the angles $\angle MPL$and$\angle QPL$ are complementary angles.

Step 4. Name the two adjacent complementary angles.

As, the angles $\angle MPL$and $\angle QPL$are adjacent angles and also complementary angles.

Therefore, the two adjacent complementary angles are$\angle MPL$ and $\angle QPL$.