Question

in the figure, ∠1 is a central angle and ∠2 is an inscribed angle. find the angle measures of 1 and 2. 125° 143° m∠1 = 143 × m∠2 = 71.5 ×

Explanation:

Step1: Recall central - angle property

The measure of a central angle is equal to the measure of the intercepted arc. Here, the arc intercepted by $\angle1$ is $143^{\circ}$, so $m\angle1 = 143^{\circ}$.

Step2: Recall inscribed - angle property

The measure of an inscribed angle is half of the measure of the intercepted arc. The arc intercepted by $\angle2$ is also $143^{\circ}$. So $m\angle2=\frac{143^{\circ}}{2}=71.5^{\circ}$.

Answer:

$m\angle1 = 143^{\circ}$, $m\angle2 = 71.5^{\circ}$