Question

Solve for x, then find each angle measure.

Answer 1

x = 13

m∠P = 126°

m∠Q = 30°

m∠R = 24°

Explanation:

The three angles of a triangle must add up to 180°

⇒ (4x - 22 ) + (10x - 4) + (x + 11) = 180

Removing parentheses and collecting like terms
⇒ 4x - 22 + 10x - 4 + x + 11 = 180

⇒ 4x + 10x + 1x -22 - 4 + 11 = 180

⇒ 15x - 15 = 180

⇒ 15x = 180 + 15

⇒ 15x = 195

⇒ x = 195/15

⇒ x = 13

m∠P = 10x - 4

= 10 x 13 - 4

= 130 - 4

= 126°

m∠P = 126°

m∠Q = 4x - 22

= 4 x 13 - 22

= 52 - 22

= 30°

m∠Q = 30°

m∠R = x + 11

= 13 + 11

= 24°

m∠R = 24°