Question

lines ac and bd intersect at point o. if m∠aod=(10x - 7)° and m∠boc=(7x + 11)°, what is m∠boc? 6° 53° 89° 106°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Since $\angle AOD$ and $\angle BOC$ are vertical angles, $m\angle AOD=m\angle BOC$. So, $10x - 7=7x + 11$.

Step2: Solve for $x$

Subtract $7x$ from both sides: $10x-7x - 7=7x-7x + 11$, which simplifies to $3x-7 = 11$. Then add 7 to both sides: $3x-7 + 7=11 + 7$, so $3x=18$. Divide both sides by 3: $x=\frac{18}{3}=6$.

Step3: Find $m\angle BOC$

Substitute $x = 6$ into the expression for $m\angle BOC$. $m\angle BOC=7x + 11=7\times6+11=42 + 11=53^{\circ}$.

Answer:

$53^{\circ}$