Question

The measure of an angle is 24 more than the measure of its supplement. How do you find the measures of both angles?

Answer 1

Hint: We are given two angles with relation to the supplement. Using the given information, we have to find the values of both the angles. We will first let that the first angle be \[x\] degrees. So, the other angle is 24 more than the first angle \[x\], such that when they are added gives the sum of the angles as supplementary, which is, \[{{180}^{\circ }}\]. Based on the given condition, we will write the expression, which becomes \[x+(x+24)={{180}^{\circ }}\]. Solving the expression further will give us the value of both the angles asked in the question.

Complete step by step solution:
According to the given question, we are given supplementary angles and based on the given information, we have to find the value of the both the angles mentioned.
We will begin by writing the given condition in a mathematical form.
Let us suppose that the first angle be \[x\] degrees,
Then the second angle is given that it is 24 more than the first angle, that is, we will have the second angle as \[(x+24)\] degrees.
And it is also given that the sum of both the angles is a supplementary angle.
Supplementary angles refers to the angles whose sum results a total of \[{{180}^{\circ }}\].
So, we have,
The sum of the two angles as \[{{180}^{\circ }}\],
\[x+(x+{{24}^{\circ }})={{180}^{\circ }}\]
We have to solve this expression in terms of \[x\], we get,
\[\Rightarrow x+x+{{24}^{\circ }}={{180}^{\circ }}\]
\[\Rightarrow 2x+{{24}^{\circ }}={{180}^{\circ }}\]
Subtracting \[{{24}^{\circ }}\] on both sides of the above expression, we get,
\[\Rightarrow 2x+{{24}^{\circ }}-{{24}^{\circ }}={{180}^{\circ }}-{{24}^{\circ }}\]
\[\Rightarrow 2x={{156}^{\circ }}\]
Dividing both the sides by 2,
\[\Rightarrow \dfrac{2x}{2}=\dfrac{{{156}^{\circ }}}{2}\]
\[\Rightarrow x={{78}^{\circ }}\]
The first angle is \[x={{78}^{\circ }}\]
The second angle is \[(x+{{24}^{\circ }})\],
\[\Rightarrow {{78}^{\circ }}+{{24}^{\circ }}={{102}^{\circ }}\]
Therefore, the first and the second angle is \[{{78}^{\circ }}\] and \[{{102}^{\circ }}\] respectively.

Note: The word to word translation of the given question may look like this, \[x={{180}^{\circ }}-(x+{{24}^{\circ }})\], solving this will also result in the same answer that we got. The mathematical expression should be carefully solved for \[x\].