The exterior angle of a triangle is congruent to the sum of the opposite interior angles
The measure of the exterior angle of the triangle is 114 degrees
From the figure,
- The interior angles are 24 and 2x + 18.
- The exterior angle is 3x + 6.
So, the interior and exterior angles have the following relationship
[tex]\mathbf{3x + 6 = 2x + 18 + 24}[/tex]
Collect like terms
[tex]\mathbf{3x - 2x = -6 + 18 + 24}[/tex]
[tex]\mathbf{x = 36}[/tex]
The exterior angle is given as:
[tex]\mathbf{\theta = 3x + 6}[/tex]
Substitute 36 for x
[tex]\mathbf{\theta = 3 \times 36 + 6}[/tex]
[tex]\mathbf{\theta = 114}[/tex]
Hence, the exterior angle is 114 degrees
Read more about exterior angles at:
https://brainly.com/question/17972372
