Question

Among two supplementary angles, the measure of the larger angle is ${44}^{\circ }$ more than the measure of the smaller. find their measure.

Answer 1

Let us suppose, smaller angle $=x^{\circ }$

then by question, larger angle $=x+{44}^{\circ }$

We know that the sum of two supplementary angles is ${180}^{\circ }$.

Therefore, $x+(x+44)={180}^{\circ }$

$\Rightarrow 2x+44=180$

$\Rightarrow 2x=180-44$

$\Rightarrow 2x=136$

$\therefore x=\frac{136}{2}={68}^{\circ }$

Hence, smaller angle $={68}^{\circ }$, and
Larger angle $=x+44=68+44={112}^{\circ }$