Question

1. determine the measure of the unknown angle in each triangle
2. list the side lengths from shortest to longest for each diagram

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Solve for part a

Let the unknown angle be \(x\). Given angles are 42° and 37°. Then \(x = 180-(42 + 37)=180 - 79 = 101^{\circ}\).

Step3: Solve for part b

Let the unknown angle be \(y\). Given angles are 58° and 80°. Then \(y=180-(58 + 80)=180 - 138 = 42^{\circ}\).

Step4: Solve for part c

Let the unknown angle be \(z\). Given angles are 78° and 30°. Then \(z = 180-(78+30)=180 - 108 = 72^{\circ}\).

Step5: Solve for part d

Let the unknown angle be \(w\). Given angles are 90° and 32°. Then \(w=180-(90 + 32)=180 - 122 = 58^{\circ}\).

Answer:

a. 101°
b. 42°
c. 72°
d. 58°