Question

1. using the triangle below, set up and solve an equation in order to find the value of x.

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \( \angle Q + \angle R + \angle S = 180^\circ \).

Step2: Substitute known angles

We know \( \angle Q = 34.6^\circ \), \( \angle R = 118^\circ \), and \( \angle S = x^\circ \). Substitute into the equation: \( 34.6 + 118 + x = 180 \).

Step3: Solve for x

First, add \(34.6\) and \(118\): \( 34.6 + 118 = 152.6 \). Then, \( 152.6 + x = 180 \). Subtract \(152.6\) from both sides: \( x = 180 - 152.6 = 27.4 \).

Answer:

\( x = 27.4 \)