Question

the diagram shows a triangle. what is the value of x?

Explanation:

Step1: Recall the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(32^{\circ}\), \(52^{\circ}\), and \(x\). Then, according to the angle - sum property of a triangle, we have the equation \(32 + 52+x=180\).

Step2: Simplify the left - hand side of the equation

First, add \(32\) and \(52\): \(32 + 52=84\). So the equation becomes \(84+x = 180\).

Step3: Solve for \(x\)

Subtract \(84\) from both sides of the equation. Using the subtraction property of equality \(x=180 - 84\).

Answer:

\(x = 96^{\circ}\)