Question

1. if two angles in a triangle measure 45 degrees and 60 degrees, what is the measure of the third angle? a. 70 degrees b. 65 degrees c. 60 degrees d. 75 degrees

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 third angle

Let the third angle be \(x\). Then \(x + 45^{\circ}+60^{\circ}=180^{\circ}\). So \(x=180^{\circ}-(45^{\circ} + 60^{\circ})\).
First, calculate \(45^{\circ}+60^{\circ}=105^{\circ}\).
Then \(x = 180^{\circ}-105^{\circ}=75^{\circ}\).

Answer:

d. 75 degrees