Question

A)
A circle has a diameter
and an inscribed angle at vertex
forming triangle
. The measureof angle
is 27°. Using what you know about inscribed angles, what is the angle measure of
?
(1 point)
AB C ABC
A B
m∠B =
º
A)
Triangle
is inscribed within a circle and has diameter line
, with the inscribed angle at
. Ifthe angle measure of
is 15°, what is the arc measure of
?
(1 point)
ABC AB C
A AC

Answer 1

I’ll assume the usual configuration: triangle ABC is inscribed with AB as a diameter.

1) If AB is a diameter then ∠C = 90° (Thales’ theorem). If m∠A = 27°, then
m∠B = 180° − 90° − 27° = 63°.

2) An inscribed angle of 15° intercepts arc AC, so the intercepted arc measure = 2 × 15° = 30°.

If your diagram labels were different, send the picture or restate the labels and I’ll adjust.