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,
[tex](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[/tex]
Thus the measure of angles are:
[tex](6x - 9) \text{ degrees } = 6(13) - 9 = 78-9 = 69 \text{ degrees }\\\\(9x - 6) \text{ degrees } = 9(13) - 6 = 117 - 6 = 111 \text{ degrees }[/tex]
Thus measure of angles are 69 degree and 111 degree
