Hi!
A linear pair is defined as two adjacent angles (two angles next to each other) that add to 180 degrees. This looks like a straight line with a slice, dividing the line into two angles.
Since the problem says "the measure of one angle is 1/3 the measure of the other angle," we can represent the angles as x and 1/3x. Since these two angles represent a linear pair, they add to 180 degrees.
With geometry, we are generally looking for a relationship between two given things, in order to write an equation and solve the missing information. The relationship here is that both angles add to 180.
So, we write an equation representing the relationship: x+1/3x=180.
Solving the equation, we can "fraction bust" to get rid of the fractions, by multiplying a 3 by each term and get rid of the denominator of the 1/3x:
3(x+1/3x)=180(3)
3x+x=540
4x=540
Then, divide both sides by 4 to get the following:
x=135
135 is one of our two angles.
To find the other, which is 1/3x, we substitute 135 in for x, to solve 1/3(135), which gives us 45.
To check our work and verify that these two angles for a a linear pair, we add them together to make sure we get 180. 135+45=180, so our algebra is correct!
Hope that helps!
