Question

(a) Find the angle which is supplementary to itself.
(b) Find the angle which is double its supplement.
[2 MARKS]

Answer 1

Solution: 1 Mark each

(a) Let the angle be x.

therefore its supplement = x (as the supplementary angles are equal)

Sum of supplementary angles is ${180}^{\circ }$

$x+x={180}^{\circ }$

$\Rightarrow x={90}^{\circ }$

(b) Let the angle be x.
Its supplement = 2x.
Sum of supplementary angles is ${180}^{\circ }$
$\therefore x+2x={180}^{\circ }$
$\Rightarrow 3x={180}^{\circ }$
$\Rightarrow x={60}^{\circ }$

$\therefore$ The angle which is double its supplement = 2x = ${120}^{\circ }$