Question

find the value of each variable in the figure on the right. x = (simplify your answer.)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. In the given triangle, we have two known angles 29° and 66°. Let the third - interior angle be \(z\). So, \(z+29^{\circ}+66^{\circ}=180^{\circ}\).

Step2: Solve for \(z\)

\(z = 180^{\circ}-(29^{\circ}+66^{\circ})=180^{\circ}-95^{\circ}=85^{\circ}\).

Step3: Use the property of vertical angles

The angle \(x\) and the interior angle \(z\) of the triangle are vertical angles. Vertical angles are equal. So \(x = z\).

Answer:

\(x = 85\)