Question

in the figure shown, points k, m, and p lie on circle j. which statement correctly compares two - angle measures in the figure?
a. 2(m∠kmp)=m∠kjp
b. 2(m∠jkm)=m∠kmp
c. 2(m∠jpm)=m∠kjp
d. 2(m∠kjp)=m∠kmp

Explanation:

Step1: Recall inscribed - central angle relationship

The measure of an inscribed angle in a circle is half the measure of the central angle that subtends the same arc. $\angle KMP$ is an inscribed angle and $\angle KJP$ is a central angle, and they subtend the same arc $\overset{\frown}{KP}$.

Step2: Apply the angle - measure formula

By the inscribed - central angle theorem, $m\angle KMP=\frac{1}{2}m\angle KJP$, or $2(m\angle KMP)=m\angle KJP$.

Answer:

A. $2(m\angle KMP)=m\angle KJP$