Question

what is the value of x in the figure below? 22.5° 45° 55° 57.5°

Explanation:

Step1: Find the adjacent interior angle

The adjacent interior angle to \(115^{\circ}\) is \(180 - 115=65^{\circ}\) (linear - pair angles).

Step2: Use the triangle - angle sum property

In a triangle, the sum of interior angles is \(180^{\circ}\). Let the angles of the triangle be \(x\), \(65^{\circ}\), and \(70^{\circ}\). Then \(x + 65+70 = 180\).

Step3: Solve for \(x\)

\(x=180-(65 + 70)\)
\(x=180 - 135\)
\(x = 45^{\circ}\)

Answer:

\(45^{\circ}\)