there is a pair of vertical angles whose measures are m<1=106 and m<2=(3x-75)

1 answer

To find the measure of angle 2, we can use the property of vertical angles which states that vertical angles are congruent (i.e., they have the same measure).
Given that angle 1 measures 106 degrees, we can set up the equation:
106 = 3x - 75
To solve for x, we isolate the variable:
3x = 106 + 75
3x = 181
x = 181/3
x = 60.33
Substituting this value back into the equation for angle 2:
m<2 = 3(60.33) - 75
m<2 = 181 - 75
m<2 = 106
Therefore, the measure of angle 2 is also 106 degrees.