Two angles form a linear pair. The measure of the smaller angle is one half the measure of the larger angle. What is the degree measure of the large angle?

Question

Wyatt Anderson · Accepted Answer

The larger angle measures at #120^o#.
The smaller one is #60^o# (one half of a larger angle).
Their sum is #180^o#, as it should for a linear pair.

Assume a larger angle measure #X^o# and a smaller one measure #Y^o#. Linear pair of angle consists of two angles, sum of which is #180^o#. Therefore, #X+Y=180#. Since a smaller angle measure as half of a larger one, #Y=1/2X# We have a system of two linear equations with two unknowns. Substitute #Y# from the second equation intot the first one anf find #X#: #X+1/2X=180# #3X=360# #X=120# - this is a larger angle. Now we can find #Y#: #Y=1/2*120=60# - this is a smaller angle.