Question

1. in the following picture, find the value of x. m∠aoc = 7x - 2, m∠aob = 2x + 8, m∠boc = 3x + 14

Explanation:

Step1: Use angle - addition postulate

$m\angle AOC=m\angle AOB + m\angle BOC$

Step2: Substitute given expressions

$7x - 2=(2x + 8)+(3x + 14)$

Step3: Simplify right - hand side

$7x - 2=2x+8 + 3x + 14$
$7x - 2=5x+22$

Step4: Solve for x

$7x-5x=22 + 2$
$2x=24$
$x = 12$

Answer:

$x = 12$