Question

w)
28°
92°
x°

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.

Let the non - adjacent interior angles of the exterior angle \(x^{\circ}\) be \(a = 28^{\circ}\) and \(b=92^{\circ}\).

The formula for the exterior - angle theorem is \(x=a + b\) (where \(x\) is the exterior angle and \(a\) and \(b\) are the non - adjacent interior angles).

Step2: Calculate the value of \(x\)

Substitute \(a = 28^{\circ}\) and \(b = 92^{\circ}\) into the formula \(x=a + b\).

\(x=28^{\circ}+92^{\circ}\)

\(x = 64^{\circ}\)

Answer:

\(64^{\circ}\)