what is m∠hij? write your answer as an integer or decimal. m∠hij = °
what is m∠hij? write your answer as an integer or decimal. m∠hij = °
Answer
Explanation:
Step1: Recall inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc. The central angle $\angle HGJ = 112^{\circ}$, and the inscribed angle $\angle HIJ$ intercepts the same arc $\overset{\frown}{HJ}$.
Step2: Calculate the measure of $\angle HIJ$
By the inscribed - angle theorem, $m\angle HIJ=\frac{1}{2}m\angle HGJ$. Since $m\angle HGJ = 112^{\circ}$, then $m\angle HIJ=\frac{112^{\circ}}{2}=56^{\circ}$.
Answer:
$56$