Question

what is m∠h? write your answer as an integer or decimal. m∠h =

Explanation:

Step1: Recall inscribed - angle formula

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Find the measure of the arc intercepted by ∠H

The sum of the arcs of a circle is 360°. Let the arc intercepted by ∠H be $x$. We know two arcs: 123° and 70°. So, $x=360-(123 + 70)=360 - 193=167^{\circ}$.

Step3: Calculate the measure of ∠H

Since the measure of an inscribed angle is half the measure of its intercepted arc, $m\angle H=\frac{1}{2}\times167^{\circ}=83.5^{\circ}$.

Answer:

$83.5$