Question

If ∠P and ∠Q are complementary angles, m∠P = 7x + 3, and m∠Q = 16x - 15, find m∠P.

Answer 1

Step-by-step explanation:

7x+3+16x-15=90°.

23-12x=90°.

90-23=-12x.

67/12=x.

Answer 2

m∠P = 41°

Given :

∠P and ∠Q are complementary angles, m∠P = 7x + 13°, and m∠Q = 16x - 15° [ Correction in the question ]

To find :

The m∠P

Solution :

Step 1 of 2 :

Form the equation

Here it is given that ∠P and ∠Q are complementary angles

m∠P = 7x + 13° , and m∠Q = 16x - 15°

We know that two angles are said to be complementary if sum of the angles = 90°

Thus we have

m∠P + m∠Q = 90°

⇒ ( 7x + 13° ) + ( 16x - 15° ) = 90°

Step 2 of 2 :

Find the required angle

( 7x + 13° ) + ( 16x - 15° ) = 90°

⇒ 23x - 2° = 90°

⇒ 23x = 92°

⇒ x = 4°

m∠P = 7x + 13° = 28° + 13° = 41°

m∠Q = 16x - 15° = 64° - 15° = 49°

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