Question

Choose the correct word and fill in the blanks :

If an angle is equal to $10°$, then its supplementary angle is an ………….. angle. (acute / obtuse).

Answer 1

Acute angle and obtuse angle :

An acute angle is an angle that measures between $0°$ and $90°$ whereas an obtuse angle is an angle that measures between $90°$ and $180°$.

Supplementary angles :

As we know that, two angles are said to be supplementary angles if they add up to $180°$. As given in the figure :

The sum of $\angle AOB$ and $\angle BOC$ is $180°$.( i.e. $\angle AOB+\angle BOC=110°+70°=180°$)

So, $\angle AOB$ and $\angle BOC$ are supplementary angles.

As per the question:

Let the measure of the supplementary angle of $10°$ be $x°$.

$10°+x°=180°$ ($\because$Supplementary angles add up to $180°$)

$\Rightarrow x°=180°-10°$ (By transposing $10°$ from L.H.S. to R.H.S.)

$\Rightarrow x°=170°$

As we have calculated the measure of the supplementary angle of $10°$ is $170°$which is an obtuse angle.

Hence if an angle is equal to $10°$, then its supplementary angle is an obtuse angle.