Question

<1 and <2 are a linear pair. M <1=x-35 and M <2=x+83. Find the measure of each angle.

answers -
<1=31, <2=149, or <1=66, <2=124

Answer 1

m<1 + m<2 = m<3
m<3 = 180
m<1 + m<2 = 180
Substitute the expressions in x for m<1 and m<2 and solve the equation for x.
Once you have x, substitute it into m<1 = x - 35 and m<2 = x + 83 to get the measure of the angles.

Answer 2

I still dont quit get how to do it /:

Answer 3

A linear pair is a pair of angles which have a common side. The non-common sides form a line.
The measures of the angles of a linear pair add up to 180 degrees.
Since you are given that <1 and <2 are a linear pair, then that means that
m<1 + m<2 = 180
You are also given that m<1 = x - 35 and m<2 = x + 83. If you substitute these two expressions in x in m<1 + m<2 = 180, you get the equation:
x - 35 + x + 83 = 180
If you solve that equation for x, then you can substitute the value of x in
m<1 = x - 35 and m<2 = x + 83 to get the measures of angles 1 and 2.