Question
In ΔQRS, start overline, Q, S, end overlineQS is extended through point S to point T, m, angle, R, S, T, equals, left bracket, 7, x, minus, 17, right bracket, degreesm∠RST=(7x−17)∘, m, angle, Q, R, S, equals, left bracket, 3, x, plus, 14, right bracket, degreesm∠QRS=(3x+14)∘, and m, angle, S, Q, R, equals, left bracket, 2, x, minus, 11, right bracket, degreesm∠SQR=(2x−11)∘. Find m, angle, Q, R, S, .m∠QRS.
Answers
GPT 3.5
Since angles in a triangle add up to 180 degrees, we have:
m∠QRS + m∠RST + m∠SQR = 180
Substituting the given expressions:
(3x + 14) + (7x - 17) + (2x - 11) = 180
Simplifying the equation:
12x - 14 = 180
Adding 14 to both sides:
12x = 194
Dividing by 12:
x = 16.17
Now we can find m∠QRS:
m∠QRS = 3x + 14
m∠QRS = 3(16.17) + 14
m∠QRS = 48.51 + 14
m∠QRS = 62.51 degrees
Therefore, m∠QRS is 62.51 degrees.
m∠QRS + m∠RST + m∠SQR = 180
Substituting the given expressions:
(3x + 14) + (7x - 17) + (2x - 11) = 180
Simplifying the equation:
12x - 14 = 180
Adding 14 to both sides:
12x = 194
Dividing by 12:
x = 16.17
Now we can find m∠QRS:
m∠QRS = 3x + 14
m∠QRS = 3(16.17) + 14
m∠QRS = 48.51 + 14
m∠QRS = 62.51 degrees
Therefore, m∠QRS is 62.51 degrees.