Question

which expression gives the measure of ∠abc? a. 110° - 20° b. $\frac{1}{2}(110° - 20°)$ c. 110° + 20° d. $\frac{1}{2}(110° + 20°)$

Explanation:

Step1: Identify angle type

Angle ABC is formed by intersecting chords inside a circle.

Step2: Apply intersecting chords theorem

The measure of such an angle is $\frac{1}{2}$ the sum of its intercepted arcs.

Step3: Calculate using given arcs

Intercepted arcs are $110^\circ$ and $20^\circ$, so $\angle ABC = \frac{1}{2}(110^\circ + 20^\circ)$.

Answer:

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