Question

find the measures of the interior angles of the triangle.
∠a = □°
∠b = □°
∠c = □°

Explanation:

Step1: Identify given angles

From the figure, $\angle A = 35^{\circ}$ and $\angle C=45^{\circ}$.

Step2: Use triangle - angle sum property

The sum of interior angles of a triangle is $180^{\circ}$. Let $\angle B=x$. Then $\angle A+\angle B+\angle C = 180^{\circ}$.
Substitute the values: $35^{\circ}+x + 45^{\circ}=180^{\circ}$.
Combine like terms: $x+80^{\circ}=180^{\circ}$.
Solve for $x$: $x=\angle B=180^{\circ}-80^{\circ}=100^{\circ}$.

Answer:

$\angle A = 35^{\circ}$, $\angle B = 100^{\circ}$, $\angle C = 45^{\circ}$