<1 and <2 are a linear pair. m<1= x-35, and m<2= x+83. Find the measure of each angle.
a. <1=31, <2=149**
b. <1=66, <2=114
c. <1=31, <2=159
d. <1=66, <2=124
correct
To find the measure of each angle, we can set the two expressions for the angle measures equal to each other and solve for x.
Given:
m<1 = x - 35
m<2 = x + 83
Since <1 and <2 are a linear pair, their measures should add up to 180 degrees.
So we can set up the equation:
m<1 + m<2 = 180
Substituting the given expressions, we have:
(x - 35) + (x + 83) = 180
Simplifying the equation:
2x + 48 = 180
2x = 132
x = 66
Now that we have found the value of x, we can substitute it back into the expressions for the angle measures:
m<1 = x - 35 = 66 - 35 = 31
m<2 = x + 83 = 66 + 83 = 149
Therefore, the measures of the angles are:
<1 = 31 degrees
<2 = 149 degrees
So, the correct answer is option a: <1 = 31, <2 = 149.