From the figure, the following are given:
Arc KL = 8x - 6
Arc MC = 7x - 10
∠KJL = 7x - 2
To be able to find the measure of ∠KJL, let's first determine the value of x. We will be using the following equation for Arc Length and Angles:
[tex]\angle KJL\text{ = }\frac{1}{2}(Arc\text{ KL + Arc MC})[/tex]We get,
[tex]7x-2\text{ = }\frac{1}{2}(8x-6\text{ + 7x - 10})[/tex][tex]7x-2\text{ = }\frac{1}{2}(15x-16)[/tex][tex](2)(7x-2)\text{ = }(15x-16)[/tex][tex]14x-4\text{ = }15x-16[/tex][tex]16-4\text{ = }15x-\text{ 14x}[/tex][tex]\text{ 12}^{\circ}\text{ = x}[/tex]Let's determine the measure of ∠KJL.
∠KJL = 7x - 2
= 7(12) - 2
= 84 - 2
∠KJL = 82°
Therefore, the measure of ∠KJL is 82°
