Question

5.find the value of x and the missing angle measure. 2x 116° 44°

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.
So, \(2x + 44^{\circ}=116^{\circ}\).

Step2: Solve for \(x\)

Subtract \(44^{\circ}\) from both sides of the equation \(2x + 44^{\circ}=116^{\circ}\).
\(2x=116^{\circ}- 44^{\circ}\)
\(2x = 72^{\circ}\)
Divide both sides by \(2\): \(x=\frac{72^{\circ}}{2}=36^{\circ}\).

Step3: Find the measure of the angle \(2x\)

Substitute \(x = 36^{\circ}\) into \(2x\).
\(2x=2\times36^{\circ}=72^{\circ}\)

Answer:

\(x = 36^{\circ}\) and the missing angle measure (\(2x\)) is \(72^{\circ}\)