Question

The measure of one of the adjacent angles is twice the other. If both the angles combined form a straight line, find the measure of each angle.

• A. ${45}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${120}^o$

Answer 1

Answer: (B), (D)

${120}^o$

Let the two angles be $a^o$ and $b^o.$
These two angles are adjacent to each other.
Also, they combinedly form a straight line.
The representation is as follows:

$\therefore a^o+b^o={180}^o$
Also, $a^o=2\times b^o$
$\Rightarrow 2b^o+b^o={180}^o$
$\Rightarrow 3b^o={180}^o$
$\Rightarrow b^o=\frac{{180}^o}{3}={60}^o$
$\Rightarrow a^o=2\times b^o=2\times {60}^o={120}^o$

$\therefore$ The angles are ${60}^o$ and ${120}^o.$