Question

An angel which is half of its supplement is of______

Answer 1

Hint: We need to find the angle which is half of its supplement. We know that the property of supplement angles states that the two angles are supplementary if and only if their sum is equal to 180 degrees. To solve this we take the angle of supplement as \[x \] . Using the conditions given we can find the value of \[x \] .

Complete step-by-step answer:
Let the angle of which of the supplement is \[x \] .
As we mentioned above that the two angles are supplementary then their sum is equal to 180 degrees.
So, if \[x \] is the angle then its supplementary angle will be \[{180^0} - x \] , because supplement angles add up to 180 degrees.
In the question they mentioned that to find the half of its supplement angle. So dividing the supplementary angle by 2. So using this we get,
 \[ \Rightarrow x = \dfrac{{{{180}^0} - x}}{2} \]
Multiply 2 on both the sides, we get,
 \[ \Rightarrow 2x = {180^0} - x \]
Separating variables and constants we get,
 \[ \Rightarrow 2x + x = {180^0} \]
 \[ \Rightarrow 3x = {180^0} \]
We need the value of \[x \] , so divide both sides by 3.
 \[ \Rightarrow x = \dfrac{{{{180}^0}}}{3} \] (Using simple division.)
 \[ \Rightarrow x = {60^0} \]
An angel which is half of its supplement is of \[{60^0} \] .
So, the correct answer is “ \[{60^0} \] ”.

Note: In order to solve this type of problem, students must consider the given angle in an unknown variable. Using the condition, create an equation and solve for the unknown variable. Similarly you can find complementary angles. Follow the same procedure as mentioned above, but their sum of angles will be equal to 90 degrees. If you solve it you will get 30 degrees which is a required answer.