Question

In ΔQRS, start overline, Q, S, end overline
QS
​
is extended through point S to point T, m, angle, R, S, T, equals, left parenthesis, 7, x, minus, 17, right parenthesis, degreesm∠RST=(7x−17)
∘
, m, angle, Q, R, S, equals, left parenthesis, 3, x, plus, 14, right parenthesis, degreesm∠QRS=(3x+14)
∘
, and m, angle, S, Q, R, equals, left parenthesis, 2, x, minus, 11, right parenthesis, degreesm∠SQR=(2x−11)
∘
. Find m, angle, Q, R, S, .m∠QRS.

Answer 1

Exterior angle theorem: m∠RST = m∠QRS + m∠SQR.

So (7x − 17) = (3x + 14) + (2x − 11) = 5x + 3.
Solve: 7x − 17 = 5x + 3 → 2x = 20 → x = 10.

Then m∠QRS = 3x + 14 = 3(10) + 14 = 44°.
Answer: 44°.