The circle below has center S. Suppose that m OR = 44º. Find the following.

(a) m2 QPR =

(b) m2 QSR =

a) m∠QPR = 22°

b) m∠QSR = 44°

Step-by-step explanation:

central angle and inscribed angle

Given measure of arc QR = 44º

We should know the following:

The measure of arc equal to the central angle containing that arc

The measure of arc equal two times the inscribed angle containing that arc

According to the previous:

a) ∠QPR is an inscribed angle opposite to the arc QR

So, m arc QR = 2 m∠QPR

∴ ∠QPR = m arc QR/2 = 44/2 = 22°

b) ∠QSR is the central angle opposite to the arc QR

So, m arc QR = m∠QSR

∴ m∠QSR = 44°