Question

the diagram shows a triangle. what is the value of x? 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 \(A = 32^{\circ}\), \(B=52^{\circ}\), and \(C = x\). Then, according to the formula \(A + B+C=180^{\circ}\).

Step2: Substitute the known values and solve for \(x\)

Substitute \(A = 32^{\circ}\) and \(B = 52^{\circ}\) into the equation \(32^{\circ}+52^{\circ}+x = 180^{\circ}\). First, calculate \(32 + 52=84\). So the equation becomes \(84^{\circ}+x=180^{\circ}\). Then, solve for \(x\) by subtracting \(84^{\circ}\) from both sides: \(x=180^{\circ}-84^{\circ}\).

Answer:

\(x = 96\)