Answer:
m∠Q is 133°
Step-by-step explanation:
The sum of the measures of the interior angles of a triangle is 180°
In ΔPQR
∵ m∠P = (x + 13)°
∵ m∠Q = (10x + 13)°
∵ m∠R = (2x - 2)°
→ By using the rule above
∴ m∠P m∠Q + m∠R = 180°
→ Substitute the measure of each angle in the equation above
∵ x + 13 + 10x + 13 + 2x - 2 = 180
→ Add the like terms in the left side
∴ (x + 10x + 2x) + (13 + 13 - 2) = 180
∴ 13x + 24 = 180
→ Subtract 24 from both sides
∵ 13x + 24 - 24 = 180 - 24
∴ 13x = 156
→ Divide both sides by 13 to find x
∴ x = 12
→ Substitute the value of x in the measure of angle Q to find it
∵ m∠Q = 10(12) + 13
∴ m∠Q = 120 + 13
∴ m∠Q = 133°
