Question

if measure of arc JI= (3x+2), measure of arc HLK= (15x+36), and measure of angle HMK=(8x-1), find the measure of arc HLK.

Answer 1

Step 1: Problem

If the measure of arc JI= (3x+2), a measure of arc HLK= (15x+36), and a measure of angle HMK=(8x-1), find the measure of arc HLK.​

Step 2: Concept

Apply secant theorem

`\text{HMK = }(1)/(2)(\text{ }JI\text{ + HLK )}`

Step 3: Method

Given data

`\begin{gathered} 8x\text{ - 1 = }(1)/(2)\text{ ( 3x + 2 + 15x - 36 )} \\ (8x\text{ - 1 ) }*\text{ 2 = 18x - 34} \\ 16x\text{ - 2 = 18x - 34} \\ 34\text{ - 2 = 18x - 16x } \\ 32\text{ = 2x} \\ x\text{ = 32/2} \\ x\text{ = 16} \end{gathered}`

The measure of arc HLK = 15x - 36

= 15(16) - 36

= 240 - 36

= 204

Step 4: Final answer

arc HLK = 204