Question

the measures of the angles of a triangle are shown in the figure below. solve for x.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(65+(5x + 14)=180 - 36\).

Step2: Simplify the equation

First, simplify the right - hand side: \(180-36 = 144\). The equation becomes \(65+5x+14 = 144\). Then combine like terms: \(5x+(65 + 14)=144\), so \(5x+79 = 144\).

Step3: Solve for \(x\)

Subtract 79 from both sides: \(5x=144 - 79\), \(5x = 65\). Divide both sides by 5: \(x=\frac{65}{5}\).

Answer:

\(x = 13\)