Question

find the measure of the given angle. 156° 124° a. 23° b. 55° c. 29° d. 40°

Explanation:

Step1: Recall inscribed - angle formula

The measure of an inscribed angle is half the measure of its intercepted arc. Let the measure of the inscribed angle $\angle NLM$ be $x$. The sum of the arcs of a circle is $360^{\circ}$. First, find the measure of the arc intercepted by $\angle NLM$. The two given arcs are $156^{\circ}$ and $124^{\circ}$. The arc intercepted by $\angle NLM$ is $360-(156 + 124)$.

Step2: Calculate the measure of the intercepted arc

$360-(156 + 124)=360 - 280=80^{\circ}$.

Step3: Use the inscribed - angle formula

Since the measure of an inscribed angle is half the measure of its intercepted arc, $x=\frac{1}{2}\times80^{\circ}$.
$x = 40^{\circ}$.

Answer:

d. $40^{\circ}$