Question

problem 20: (lesson 10) if $overrightarrow{oa}-overrightarrow{ob}-overrightarrow{oc}$ and if $mangle aob = 9x + 20$, $mangle boc = 7x - 6$, and $mangle aoc = 142$, then find $mangle boc$. after you enter your answer press go. $mangle boc =$

Explanation:

Step1: Use angle - addition postulate

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

Step2: Substitute given expressions

$142=(9x + 20)+(7x - 6)$

Step3: Simplify the right - hand side

$142=9x+20 + 7x-6$
$142=16x + 14$

Step4: Solve for x

$16x=142 - 14$
$16x=128$
$x = 8$

Step5: Find m∠BOC

$m\angle BOC=7x - 6$
Substitute $x = 8$: $m\angle BOC=7\times8-6=56 - 6=50$

Answer:

50