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?

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Answer 1 · 2015-12-01T16:12:11

$120^@$

Angles in a linear pair form a straight line with a total degree measure of $180^@$ .

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

Smaller angle $=x^@$
Larger angle $=2x^@$

Since the sum of the angles is $180^@$ , we can say that $x+2x=180$ .

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

Thus, the larger angle is $(2xx60)^@$ , or $120^@$ .