Question

Find the measure of the angle(s). 2x (5x - 2) 76°

Answer 1

To solve this problem we need to understand two concepts. The first one is that an external angle on a triangle is suplementary to the internal angle next to it. The other concept is that the sum of all the internal angles on a triangle is equal to 180 degrees. With this in mind we can solve the problem.

We were given two internal angles the first one is 76 degrees and the second one is 2x degrees. We were also given an external angle that measures 5x -2 degrees. The internal angle that is closer to the external angle given can be represented as:

`180-(5x-2)=180+2-5x=182-5x`

This angle is equal to 182 -5x degrees. If we add all the internal angles on the triangle we need to have 180 degrees.

`\begin{gathered} 182-5x+2x+76=180 \\ 258-3x=180 \\ -3x=180-258 \\ -3x=-78 \\ x=(-78)/(-3)=26 \end{gathered}`

The value of "x" is equal to 26 degrees. Therefore the angles are:

`\begin{gathered} \text{ internal=2}\cdot26=52\text{ degrees} \\ \text{ external = 5}\cdot26-2=128\text{ degrees} \end{gathered}`