Question

The support for a window air-conditioning unit forms a triangle and an exterior angle. What is the measure of the exterior angle?

Answer 1

Let the exterior angle be y.

We know that the exterior angle is the sum of opposite two interior angles.

Therefore, y = 3x + 90            --- (1)

Also, y and 5x - 6 are linear pair.

Therefore, y + (5x - 6) = 180

Substituting y = 3x + 90 from (1), we get,

                 (3x + 90) + (5x - 6) = 180

                 8x + 84 = 180

                 8x = 180 - 84 = 96

                  x = 12 degrees

Hence, exterior angle y = 3(12) + 90 = 126 degrees.

Answer 2

In the diagram is shown right triangle with angles of measures $3x^{\circ}$ and $(5x-6)^{\circ}.$ These two angles are complementary, then

$3x^{\circ}+(5x-6)^{\circ}=90^{\circ}.$

Solve this equation:

$3x+5x-6=90,\\ \\8x=90+6,\\ \\8x=96,\\ \\x=\dfrac{96}{8}=12.$

Therefore, $3x^{\circ}=36^{\circ}$ and $(5x-6)^{\circ}=54^{\circ}.$

Now find measures of exterior angles:

• the measure of exterior angle that is adjacent to the angle $36^{\circ}$ is $180^{\circ}-36^{\circ}=144^{\circ};$
• the measure of exterior angle that is adjacent to the angle $54^{\circ}$ is $180^{\circ}-54^{\circ}=126^{\circ}.$