Question

100pts Find mPQ in the circle to the right

Answer 1

We need indirectly m<POQ

See NR is a straight line so the three angles situated underneath are linear pair and supplementary

m<POQ

• 180-(82+63)
• 180-145
• 35°

Answer 2

C) 35°

Explanation:

From inspection of the given diagram, it appears that the line segment NOR is the diameter of the circle (where point O is the center).

Angles on a straight line sum to 180°

⇒ ∠NOP + ∠POQ + ∠QOR = 180°

⇒ 82° + ∠POQ + 63° = 180°

⇒ ∠POQ = 180° - 82° - 63°

⇒ ∠POQ = 35°

As an arc measure equals its corresponding central angle measure:

`\sf \implies \overset{\frown}{PQ}= \angle POQ`

`\sf \implies \overset{\frown}{PQ}=35^(\circ)`