Question

question 8 of 10 which expression gives the measure of ∠abc? a. 1/2(110° + 20°) b. 110° + 20° c. 110° - 20° d. 1/2(110° - 20°)

Explanation:

Step1: Recall the inscribed - angle theorem for angles formed by two chords

The measure of an angle formed by two chords in a circle is half the difference of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The larger intercepted arc is $110^{\circ}$ and the smaller intercepted arc is $20^{\circ}$.

Step3: Apply the formula

The measure of $\angle ABC=\frac{1}{2}( \text{measure of larger arc}-\text{measure of smaller arc})=\frac{1}{2}(110^{\circ}-20^{\circ})$.

Answer:

D. $\frac{1}{2}(110^{\circ}- 20^{\circ})$