Question

Which two angles in the figure are obtuse angles?

Answer 1

Answer: C. ∠SQP and ∠TQR

Step-by-step 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.