Question

1. p 74° r m∠q = m∠r =

Explanation:

Step1: Identify isosceles triangle

Since two sides of $\triangle PQR$ are equal (marked with the same tick - marks), $\triangle PQR$ is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal, so $\angle R=\angle P = 74^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle Q=x$. Then $m\angle P + m\angle Q+m\angle R=180^{\circ}$. Substitute $m\angle P = 74^{\circ}$ and $m\angle R = 74^{\circ}$ into the equation: $74^{\circ}+x + 74^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle Q$

First, simplify the left - hand side of the equation: $148^{\circ}+x=180^{\circ}$. Then subtract $148^{\circ}$ from both sides: $x=m\angle Q=180^{\circ}-148^{\circ}=32^{\circ}$.

Answer:

$m\angle R = 74^{\circ}$, $m\angle Q = 32^{\circ}$