Question

b. m(∠boc)=□° and m(∠aob)=□°
m(∠aob) is 30° less than 4m(∠boc)

Explanation:

Step1: Let $m(\angle BOC)=x$ and $m(\angle AOB)=y$.

We know that $y = 4x-30$ and also $x + y=90$ (since $\angle AOC = 90^{\circ}$).

Step2: Substitute $y$ in the second - equation.

Substitute $y = 4x - 30$ into $x + y=90$. We get $x+(4x - 30)=90$.

Step3: Simplify the equation.

Combine like - terms: $x + 4x-30=90$, which simplifies to $5x-30 = 90$.

Step4: Solve for $x$.

Add 30 to both sides of the equation: $5x=90 + 30=120$. Then divide both sides by 5, so $x=\frac{120}{5}=24$.

Step5: Solve for $y$.

Substitute $x = 24$ into $y = 4x-30$. Then $y=4\times24-30=96 - 30=66$.

Answer:

$m(\angle BOC)=24^{\circ}$ and $m(\angle AOB)=66^{\circ}$