Question

properties of isosceles triangles
score: 2/3 penalty: none
question
in △opq, $overline{op}congoverline{qo}$ and m∠o = 65°. find m∠q.
answer attempt 1 out of 2

Explanation:

Step1: Recall isosceles - triangle property

Since $\overline{OP}\cong\overline{QO}$ in $\triangle OPQ$, $\angle P=\angle Q$.

Step2: Use angle - sum property of a triangle

The sum of interior angles of a triangle is $180^{\circ}$. So, $m\angle O + m\angle P+m\angle Q = 180^{\circ}$. Substitute $m\angle P = m\angle Q$ and $m\angle O=65^{\circ}$ into the equation: $65^{\circ}+m\angle Q + m\angle Q=180^{\circ}$.

Step3: Solve for $m\angle Q$

Combine like - terms: $65^{\circ}+2m\angle Q = 180^{\circ}$. Then, $2m\angle Q=180^{\circ}- 65^{\circ}=115^{\circ}$. Divide both sides by 2: $m\angle Q=\frac{115^{\circ}}{2}=57.5^{\circ}$.

Answer:

$57.5^{\circ}$