Question

which theorem states that any angle inscribed in a semi - circle is a right angle?
a. perpendicular bisector theorem
b. inscribed angle theorem
c. tangent - radius theorem
d. thales theorem
if an inscribed angle intercepts an arc of 80°, what is the measure of the inscribed angle?
a. 20°
b. 80°
c. 60°
d. 40°
what is the measure of an inscribed angle that intercepts a 160° arc?
a. 320°
b. 40°
c. 80°
d. 160°

Explanation:

Step1: Recall Thales' Theorem

Thales' Theorem states that any angle inscribed in a semi - circle is a right angle.

Step2: Recall inscribed - angle formula

The measure of an inscribed angle is half the measure of the intercepted arc. For an arc of $80^{\circ}$, the inscribed - angle measure is $\frac{80^{\circ}}{2}=40^{\circ}$.

Step3: Apply inscribed - angle formula again

For an arc of $160^{\circ}$, the measure of the inscribed angle is $\frac{160^{\circ}}{2}=80^{\circ}$.

Answer:

1. d. Thales' Theorem
2. d. $40^{\circ}$
3. c. $80^{\circ}$