Question

Which two angles in the figure are obtuse angles?

A. ∠SQT and ∠SQR
B. ∠TQP and ∠TQR
C. ∠SQP and ∠TQR
D. ∠SQP and ∠SQR

Answer 1

Answer: C. ∠SQP and ∠TQR

Explanation:

Since, by the given diagram,

m∠TQR = m∠SQP (vertical angles)

And, m∠TQP < m∠TQR

By adding ∠TQR on both sides,

m∠TQP + m∠TQR < m∠TQR+m∠TQR

⇒m∠TQP + m∠TQR < 2 ∠TQR

⇒ 180° < 2 m∠TQR ( Because ∠TQP and ∠TQR are linear angles)

⇒ 90° < m∠TQR

Hence ∠TQR is a obtuse angle,

⇒ ∠SQP also is a obtuse angle.