Question

given
oa ⊥ oc
m∠boc = 6x - 6°
m∠aob = 5x + 8°
find m∠boc:

Explanation:

Step1: Use perpendicular - angle property

Since $\overline{OA}\perp\overline{OC}$, then $\angle AOC = 90^{\circ}$. And $\angle AOC=\angle AOB+\angle BOC$. So, $(5x + 8)+(6x - 6)=90$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $5x+6x+8 - 6=90$, which simplifies to $11x + 2=90$.

Step3: Solve for $x$

Subtract 2 from both sides: $11x=90 - 2=88$. Then divide both sides by 11, so $x = 8$.

Step4: Find $m\angle BOC$

Substitute $x = 8$ into the expression for $\angle BOC$. $m\angle BOC=6x - 6$. So, $m\angle BOC=6\times8-6=48 - 6=42^{\circ}$.

Answer:

$42^{\circ}$