Find the measure of Angle 6.
measure of angle 7 = 2x+15
measure of angle 8 = 3x
To find the measure of Angle 6, we need to use the information about Angle 7 and Angle 8.
Given:
Measure of Angle 7 = 2x + 15
Measure of Angle 8 = 3x
To find the measure of Angle 6, we need to use the fact that the sum of the measures of angles in a triangle is 180 degrees.
In this case, the sum of the measures of Angle 6, Angle 7, and Angle 8 is 180 degrees.
So, we can write the equation:
Angle 6 + Angle 7 + Angle 8 = 180
Substituting the given values:
Angle 6 + (2x + 15) + (3x) = 180
Now, we can solve this equation to find the measure of Angle 6.
Combine like terms:
Angle 6 + 2x + 15 + 3x = 180
Angle 6 + 5x + 15 = 180
Angle 6 + 5x = 180 - 15
Angle 6 + 5x = 165
Simplify:
5x + Angle 6 = 165
Angle 6 = 165 - 5x
Therefore, the measure of Angle 6 is 165 - 5x.