Question

1. determine the value of x in the diagram. enter your answer in the box. x= °

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Set up an equation

Let the third - angle of the triangle be \(y\). First, find \(y\). The non - interior angle 152° and \(y\) are supplementary. So \(y = 180 - 152=28^{\circ}\).
Then, using the angle - sum property of a triangle \(x + y+17^{\circ}=180^{\circ}\). Substitute \(y = 28^{\circ}\) into the equation: \(x+28^{\circ}+17^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\(x=180-(28 + 17)\)
\(x = 180 - 45\)
\(x = 135^{\circ}\)

Answer:

\(135\)