Find the measures of and

Mathematics

1 answer:

3241004551 [841]3 years ago

8 0

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°

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