Angle P = 90°
Angle Q = 61°
Angle R = 29°
The sum of the three interior angles in a triangle is 180°. Right angles measure 90°, so angle P is 90°. 180° - 90° = 90°, so the sum of the two remaining angles is 90°.
angle R + angle Q = 90°
(3x - 4)° + (2x + 39)° = 90°
3x - 4 + 2x + 39 = 90
5x + 35 = 90
5x = 55
x = 11
angle R is (3x - 4)°
3(11) - 4 =
33 - 4 = 29°
angle Q is (2x + 39)°
2(11) + 39 =
22 + 39 = 61°
90° + 29° + 61° = 180°