Question

Find each indicated measure and show steps please

Answer 1

94…………………………………………….

Answer 2

m∠N = 72°

mNQ = 94°

Explanation:

An inscribed angle is equal to half the measure of its intercepted arc

∠N is an inscribed angle and arc MP is it's intercepted arc

Thus, ∠N = 1/2 arc MP

if arc MP = 144

Then ∠N = 144/2

144/2 = 72

Hence, ∠N = 72°

For ∠P and arc NQ we are given the measure of the inscribed angle and need to find the measure of the intercepted arc.

If the measure of an inscribed angle equals half the measure of its intercepted arc, then the measure of the intercepted arc equals twice the measure of the inscribed angle.

Thus, arc mNQ = 2(∠P)

If ∠P = 47, then mNQ = 2(47)

2 * 47 = 94

Hence, mNQ = 94