and are a linear pair. m
= x – 30, and m = x + 76.
Find the measure of each angle.
(1 point)
= 67, = 123
= 37, = 153
= 37, = 143
= 67, = 113
To find the measures of the angles, we use the linear pair property, which states that the measures of two adjacent angles that form a linear pair sum up to 180 degrees.
So, we have:
Angle 1 (m1) = x - 30
Angle 2 (m2) = x + 76
Since these angles are a linear pair, we can set up the equation:
Angle 1 + Angle 2 = 180
(x - 30) + (x + 76) = 180
2x + 46 = 180
2x = 180 - 46
2x = 134
x = 67
Now, we can substitute x back into the expressions for Angle 1 and Angle 2 to find their measures:
Angle 1 (m1) = x - 30 = 67 - 30 = 37
Angle 2 (m2) = x + 76 = 67 + 76 = 143
Therefore, the measure of Angle 1 is 37 degrees and the measure of Angle 2 is 143 degrees.
Option C, = 37, = 143, is the correct answer.