Question

find the value of x. then find the measure of each angle and write the answers in ascending order.

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.
So, \(5x + 62=(3x + 47)+37\)

Step2: Simplify the right - hand side

\(5x + 62=3x+47 + 37\)
\(5x + 62=3x + 84\)

Step3: Subtract \(3x\) from both sides

\(5x-3x+62=3x - 3x+84\)
\(2x+62 = 84\)

Step4: Subtract 62 from both sides

\(2x+62-62=84 - 62\)
\(2x=22\)

Step5: Solve for \(x\)

Divide both sides by 2: \(x=\frac{22}{2}=11\)

Step6: Find the measure of each angle

• First angle: \(37^{\circ}\)
• Second angle: \(3x + 47\). Substitute \(x = 11\), \(3\times11+47=33 + 47=80^{\circ}\)
• Third angle: \(5x + 62\). Substitute \(x = 11\), \(5\times11+62=55+62 = 117^{\circ}\)

Answer:

\(x = 11\); \(37^{\circ}\); \(80^{\circ}\); \(117^{\circ}\)