Question

the measures of the angles of a triangle are shown in the figure below. solve for x. answer attempt 1 out of 2

Explanation:

Step1: Recall the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(61^{\circ}+74^{\circ}+x^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

\(61 + 74+x=180\). First, calculate \(61 + 74\): \(61+74 = 135\). Then the equation becomes \(135+x=180\).

Step3: Solve for \(x\)

Subtract \(135\) from both sides of the equation \(135+x - 135=180 - 135\). So, \(x=45\).

Answer:

\(x = 45\)