Answer:
Angle 5 = 51 degrees
Angle 6 = 129 degrees
Explanation:
When dealing with parallel lines like this, the picture attached shows all the angles that are equal to each other. Angle 6 and (3x-15) will sum to 180 degrees. Angle 5 is equal to 3x-15. (3x-15) will be equal to (2x+7)
The first step to solving this problem after the angle relationships are determined is to solve for x:
3x-15=2x+7
3x-2x=7+15
x=22
The second step is to determine angle 5:
angle 5 = 3x-15
angle 5 = 3(22)-15
angle 5 = 66-15
angle 5 = 51 degrees
The third step is to determine angle 6:
angle 6 = 180 - (3x-15)
angle 6 = 180 - 3x + 15
angle 6 = 195 - 3x
angle 6 = 195 - 3(22)
angle 6 = 195 - 66
angle 6 = 129 degrees
The final step is to check the angles. Angle 6 and 3x-15 should add to 180; 180 - angle 5 should be equal to angle 6.
129 + 3x - 15 =? 180
129 + 3(22) - 15 =? 180
129 + 66 - 15 =? 180
180 = 180
180 - 51 =? 129
180 - 51 =? 129
180 - 51 =? 129
129 = 129