Question

finding angle measures find the measure of the numbered angles. 33.

Explanation:

Step1: Find angle 1

Use the triangle angle sum theorem ($180^{\circ}$).
$$180^{\circ}-45^{\circ}-56^{\circ}=79^{\circ}$$

Step2: Find angle 2

Use the fact that angles on a straight line sum to $180^{\circ}$.
$$180^{\circ}-79^{\circ}-50^{\circ}=51^{\circ}$$

Step3: Find angle 3

Use the triangle angle sum theorem ($180^{\circ}$) for the right - angled triangle.
$$180^{\circ}-90^{\circ}-51^{\circ}=39^{\circ}$$

Answer:

$\angle1 = 79^{\circ}$, $\angle2 = 51^{\circ}$, $\angle3 = 39^{\circ}$