what is m∠hji? write your answer as an integer or decimal. m∠hji = °
what is m∠hji? write your answer as an integer or decimal. m∠hji = °
Answer
Explanation:
Step1: Find the measure of arc HI
The measure of an arc is equal to the measure of its central - angle. The central - angle corresponding to arc HI is the non - reflex angle at K. The non - reflex angle at K is $360-(94 + 118)=360 - 212=148^{\circ}$. So, the measure of arc HI is $148^{\circ}$.
Step2: Use the inscribed - angle theorem
The measure of an inscribed angle is half the measure of the intercepted arc. $\angle HJI$ is an inscribed angle that intercepts arc HI. By the inscribed - angle theorem, $m\angle HJI=\frac{1}{2}\text{ measure of arc }HI$. Since the measure of arc HI is $148^{\circ}$, then $m\angle HJI=\frac{148}{2}=74^{\circ}$.
Answer:
$74$