Question

suppose $moverparen{kli}=132^{circ}$ and $mangle lkj = 49^{circ}$. find the following. (a) $mangle kli=114^{circ}$ (b) $mangle lij=square^{circ}$

Explanation:

Step1: Recall inscribed - angle theorem

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

Step2: Find the measure of $\angle LIJ$

The arc $\overset{\frown}{LKJ}$ is the intercepted arc for $\angle LIJ$. The measure of the whole - circle is $360^{\circ}$. Given $m\overset{\frown}{KLI}=132^{\circ}$, then $m\overset{\frown}{LKJ}=360^{\circ}-132^{\circ}=228^{\circ}$.
By the inscribed - angle theorem, $m\angle LIJ=\frac{1}{2}m\overset{\frown}{LKJ}$.
So $m\angle LIJ = \frac{1}{2}\times228^{\circ}=114^{\circ}$.

Answer:

$114$