Question

One angle of a linear pair is twice the other. What is the value of the smaller angle?

• A. ${120}^{\circ }$
• B. ${50}^{\circ }$
• C. ${40}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is D ${60}^{\circ }$

A linear pair is a pair of adjacent angles that sum up to ${180}^{\circ }$

$\angle ABD+\angle DBC={180}^{\circ }$
$\angle DBC=2\angle ABD$
$\angle ABD+2\angle ABD={180}^{\circ }$
$3\angle ABD={180}^{\circ }$
$\angle ABD={60}^{\circ }$
then, $\angle DBC={120}^{\circ }$