Question

Investigate the pattern in the circle.
is a right triangle inscribed in circle
such that chord
is a diameter. Find the measure of
if arc
is 62 degrees.
(1 point)
△ABC R AB
∠ABC BC
is 31 degrees.
∠
A
B
C
is 90 degrees.
∠
A
B
C
is 59 degrees.
∠
A
B
C
is 118 degrees.

Answer 1

Answer: 31°

Reason: An inscribed angle measures half the measure of its intercepted arc. ∠ABC intercepts arc AC, which is 62°, so ∠ABC = 62°/2 = 31°. (Note: AB being a diameter implies the angle at C is 90°, but that isn't needed to find ∠ABC.)