Question

in the triangle shown below, what is x, the measure of the third angle?
20°
45°
95°
105°
(image of a triangle with angles 20°, 115°, and x)

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, if the angles of the triangle are \(20^{\circ}\), \(115^{\circ}\), and \(x\), then \(20 + 115+x=180\).

Step2: Solve for \(x\)

First, simplify the left - hand side of the equation: \(20 + 115=135\). Then the equation becomes \(135+x = 180\). Subtract 135 from both sides: \(x=180 - 135\).

Answer:

\(45^{\circ}\)