Answer:
51° and 96°
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
Angle 17x - 1 is an exterior angle, thus
17x - 1 = 33 + 10x + 1, that is
17x - 1 = 10x + 34 ( subtract 10x from both sides )
7x - 1 = 34 ( add 1 to both sides )
7x = 35 ( divide both sides by 7 )
x = 5
Hence
∠PQR = 10x + 1 = (10 × 5) + 1 = 50 + 1 = 51°
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 angles from 180 for ∠PRQ, that is
∠PRQ = 180° - (33 + 51)° = 180° - 84° = 96°
