Question

the measure of the inscribed angle PQR is 40°. What is the measure of arc AXB intercepted by it​ PLEASE HELP​

Answer 1

Step-by-step explanation:

(1) arc AXB and arc APB are semi-circular arcs.

The measure of the semicircular arc AXB is 180°.

∠APB is inscribed in the arc APB, arc AXB is an arc intercepted by it.

∴ m∠APB = 12 × m (arc AXB)

= 12 × 180 = 90°

∴ m∠APB = 90°

(2) Measure of intercepted arc = 2 × Measure of inscribed angle

Measure of inscribed angle in arc PYB = 40°

⇒ Measure of intercepted arc = 80°

∴ m(arc PY) = 80°

(3) Measure of intercepted arc = 2 × Measure of inscribed angle

Measure of inscribed angle in arc AZP = 50°

⇒ Measure of intercepted arc = 100°

∴ m( arc AZP) = 100°