# 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 larger angle?

Dec 1, 2015

${120}^{\circ}$

#### Explanation:

Angles in a linear pair form a straight line with a total degree measure of ${180}^{\circ}$.

If the smaller angle in the pair is one half the measure of the larger angle, we can relate them as such:

Smaller angle$= {x}^{\circ}$
Larger angle$= 2 {x}^{\circ}$

Since the sum of the angles is ${180}^{\circ}$, we can say that $x + 2 x = 180$.

This simplifies to be $3 x = 180$, so $x = 60$.

Thus, the larger angle is ${\left(2 \times 60\right)}^{\circ}$, or ${120}^{\circ}$.