Question

1. determine the measure of the unknown angle in each triangle.

a.
b.
c.
d.

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Calculate the unknown angle in part a

For triangle \(ABC\), let \(\angle B=x\). Then \(x + 78^{\circ}+37^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(78^{\circ} + 37^{\circ})=180^{\circ}-115^{\circ}=65^{\circ}$$

Step3: Calculate the unknown angle in part b

For triangle \(PQR\), let \(\angle R = y\). Then \(y+80^{\circ}+66^{\circ}=180^{\circ}\).

$$y=180^{\circ}-(80^{\circ}+66^{\circ})=180^{\circ}-146^{\circ}=34^{\circ}$$

Step4: Calculate the unknown angle in part c

For triangle \(MLK\), let \(\angle L=z\). Then \(z + 28^{\circ}+35^{\circ}=180^{\circ}\).

$$z=180^{\circ}-(28^{\circ}+35^{\circ})=180^{\circ}-63^{\circ}=117^{\circ}$$

Step5: Calculate the unknown angle in part d

For triangle \(GFE\), let \(\angle G = w\). Then \(w+90^{\circ}+37^{\circ}=180^{\circ}\).

$$w=180^{\circ}-(90^{\circ}+37^{\circ})=180^{\circ}-127^{\circ}=53^{\circ}$$

Answer:

a. \(65^{\circ}\)
b. \(34^{\circ}\)
c. \(117^{\circ}\)
d. \(53^{\circ}\)