Question

1. ∠bod is a right angle. m∠boc = 2x + 2 and m∠cod = x + 1. what is the measure of ∠aoe? a. 29° b. 30° c. 32° d. 60°

Explanation:

Step1: Use angle - sum property

Since $\angle BOD$ is a right - angle ($90^{\circ}$), and $\angle BOC+\angle COD = \angle BOD$. We have the equation $(2x + 2)+(x + 1)=90$.

Step2: Combine like terms

Combining like terms in the left - hand side of the equation, we get $2x+x+2 + 1=90$, which simplifies to $3x+3 = 90$.

Step3: Solve for $x$

Subtract 3 from both sides: $3x=90 - 3=87$. Then divide both sides by 3: $x=\frac{87}{3}=29$.

Step4: Find vertical angles

$\angle AOE$ and $\angle COD$ are vertical angles. Since $\angle COD=x + 1$ and $x = 29$, then $\angle COD=29+1=30^{\circ}$. And $\angle AOE=\angle COD = 30^{\circ}$ (vertical angles are equal).

Answer:

B. $30^{\circ}$