Question

Find the supplement of each of the following angles:
(i) ${80}^{\circ }$

(ii) ${54}^{\circ }$

(iii) ${105}^{\circ }$

(iv) ${123}^{\circ }$

Answer 1

(i)

The given angle measures ${80}^{\circ }$

Let the measure of its supplement be $x$.
$x+{80}^{\circ }={180}^{\circ }$
$\Rightarrow x=(180-80{)}^{\circ }={100}^{\circ }$
Hence, the supplement of the given angle will be ${100}^{\circ }$.
(ii)

The given angle measures ${54}^{\circ }$.
Let the measure of its supplement be $x$.
$x+{54}^{\circ }={180}^{\circ }$
$\Rightarrow x=(180-54{)}^{\circ }={126}^{\circ }$
Hence, the supplement of the given angle will be ${126}^{\circ }$.
(iii)

The given angle measures ${105}^{\circ }$.
Let the measure of its supplement be $x$.
$x+{105}^{\circ }={180}^{\circ }$
$\Rightarrow x=(180-105)°={75}^{\circ }$
Hence, the supplement of the given angle will be ${75}^{\circ }$.
(iv)
The given angle measures ${123}^{\circ }$.
Let the measure of its supplement be $x$.
$x+{123}^{\circ }={180}^{\circ }$
$x=(180-123{)}^{\circ }={57}^{\circ }$
Hence, the supplement of the given angle will be ${57}^{\circ }$.