Question

Among two supplementary angles, the measure of the larger angle is \[{44^0}\] more than the measure of the smaller. Find their measurement.

Answer 1

Hint- In order to solve this question first we will assume the smaller angle as a variable then by question statement we will write larger angle and in order to proceed further we will use the property as the sum of supplementary angles is always 180 degree.

Complete step-by-step answer:
Given that among two supplementary angles the measure of the larger angle is ${44^0}$ more than the measure of the smaller.
Let the smaller angle be
So, larger angle $ = x + {44^0}$
Supplementary angles are two angles whose sum is ${180^0}$
We know that sum of supplementary angles is always ${180^0}$
Smaller angle $ + $ larger angle $ = {180^0}$
$
   \Rightarrow x + x + {44^0} = {180^0} \\
   \Rightarrow 2x = {180^0} - {44^0} \\
   \Rightarrow x = \dfrac{{{{136}^0}}}{2} = {68^0} \\
$
Thus the smaller angle is ${68^0}$
Larger angle is
\[
  x + {44^0} \\
   = {68^0} + {44^0} \\
   = {112^0} \\
\]
Hence, the smaller and larger angles are ${44^0}{\text{ and 11}}{{\text{2}}^0}.$

Note- In order to solve these types of problems, first of all remember all the properties of angles and parallel lines. Be familiar with some of these terms like supplementary angles and complementary angles.
Learn about vertically opposite angles, alternate angles and corresponding angles. Learn how to solve linear equations with single variables. This will help in solving this type of question.