Question

In this picture, m∠PQR = 166° and m∠SQR = 37°. If m∠PQS = (2x + 15)°, what is the value of x?

Answer 1

In this picture, m∠PQR = 166° and m∠SQR = 37°. If m∠PQS = (2x + 15)°, what is the value of x?
A. 129
B. 114
C. 57
D. 94

Answer 2

Since angles PQR and SQR form a linear pair, their measures add up to 180°.

m∠PQR + m∠SQR = 180°
166° + 37° = 180°

Therefore, m∠PQS = (2x + 15)° = 180° - (166° + 37°)
= 180° - 203°
= -23°

Since angles cannot have negative measures, we know that this angle must have been mislabeled or measured incorrectly. Without more information or another angle measure with which to cross-reference, we cannot accurately determine the value of x.

Answer 3

Since angles PQR and SQR form a linear pair, their measures add up to 180°.

m∠PQR + m∠SQR = 180°
166° + 37° = 180°

Therefore, m∠PQS = (2x + 15)° = 180° - (166° + 37°)
= 180° - 203°
= -23°

Since angles cannot have negative measures, we know that this angle must have been mislabeled or measured incorrectly. Without more information or another angle measure with which to cross-reference, we cannot determine the value of x. The answer choices provided (A, B, C, D) are not helpful in solving for x.