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# What is the measure of an angle whose measure is ${32^\circ}$ less than its supplement?

Last updated date: 04th Aug 2024
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Hint: An angle can be defined as the figure formed by two rays meeting at a common endpoint. An angle is represented by $\angle$. When a transverse line intersects the line angle is also formed. Supplement angles are those angles whose sum of the two angles is ${180^\circ}$.

Complete step-by-step solution:
Given,
Let the measure of an angle, $a = x$
Then the other angle is $b = x + 32$
Here angle a is ${32^\circ}$ less than the b as given in the question.
Then measure of their supplement angles is
As we know that,
$\text{Supplementary angle} = {180^o} - \text{Angle given}$
$\Rightarrow a = 180 - b$
Put the value
$\Rightarrow a + b = 180$
Put the value
$\Rightarrow x + x + 32 = 180$
Simplify,
$\Rightarrow x + x = 180 - 32$
$\Rightarrow 2x = {148^o}$
$\Rightarrow x = \dfrac{{148}}{2}$
$\Rightarrow x = {74^o}$

Note: There are various types of angles. They are- right angle, acute angle, obtuse angle, straight angle, reflex angle. Complementary angles are those, in which the sum of two angles are 90. Reflex angles are those, in which the sum of two angles are equal to 270. Right angle in which angle is 90.