Question

-24°
(2x + 18)
(3x + 6)
The measure of the exterior angle of the triangle is

Answer 1

The exterior angle is 114

Answer 2

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

$\mathbf{3x + 6 = 2x + 18 + 24}$

Collect like terms

$\mathbf{3x - 2x = -6 + 18 + 24}$

$\mathbf{x = 36}$

The exterior angle is given as:

$\mathbf{\theta = 3x + 6}$

Substitute 36 for x

$\mathbf{\theta = 3 \times 36 + 6}$

$\mathbf{\theta = 114}$

Hence, the exterior angle is 114 degrees

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