Question

1) ACT Prep: Linear Pair angles have measures (6x -9)°and (9x-6)° 1.

Sketch and solve for the angle measures. Your choices will only have one angle listed.
A) 15° B) 30°C) 11° D) 69°E) 105°

Answer 1

The measure of angles are 69 degree and 111 degree

Solution:

Given is linear pair angles

The measure of angles are: (6x - 9) degrees and (9x - 6) degrees

A linear pair of angles is formed when two lines intersect.

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Therefore,

`(6x - 9) + (9x - 6) = 180\\\\\text{Remove the parenthesis and solve}\\\\6x - 9 + 9x - 6 = 180\\\\\text{Combine the like terms}\\\\6x + 9x - 15 = 180\\\\15x - 15 = 180\\\\\text{Move the constants to right side}\\\\15x = 180 + 15\\\\15x = 195\\\\x = 13`

Thus the measure of angles are:

`(6x - 9) \text{ degrees } = 6(13) - 9 = 78-9 = 69 \text{ degrees }\\\\(9x - 6) \text{ degrees } = 9(13) - 6 = 117 - 6 = 111 \text{ degrees }`

Thus measure of angles are 69 degree and 111 degree