Question

find the measure of the exterior angle. (2x + 11)° x° 44°

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(2x + 11=x + 44\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation:
\(2x+11 - x=x + 44 - x\)
\(x+11 = 44\)
Then subtract 11 from both sides:
\(x+11-11=44 - 11\)
\(x = 33\)

Step3: Find the measure of the exterior angle

Substitute \(x = 33\) into \(2x + 11\).
\(2x+11=2\times33 + 11\)
\(=66+11\)
\(=77\)

Answer:

\(77^{\circ}\)