Question

6 the measure of ∠aoc is 90°. find the value of m.

Explanation:

Step1: Set up an equation based on angle - sum

Since $\angle AOC = 90^{\circ}$, and $\angle AOC=(m + 7)+2m+11$. So we have the equation $(m + 7)+2m+11 = 90$.

Step2: Combine like - terms

Combine the $m$ terms and the constant terms on the left - hand side: $(m+2m)+(7 + 11)=90$, which simplifies to $3m+18 = 90$.

Step3: Isolate the variable term

Subtract 18 from both sides of the equation: $3m+18-18=90 - 18$, getting $3m=72$.

Step4: Solve for $m$

Divide both sides of the equation by 3: $\frac{3m}{3}=\frac{72}{3}$, so $m = 24$.

Answer:

$24$