Question

The measure of an angle which is 9 times its supplement is?

Answer 1

Hint:
To find the supplement we will understand the question, the question says an angle is 9 times of its supplement. So, we will take the actual angle as x and then we will use a supplement. This will provide us the answer.

Complete step by step solution:
Let the required angle be x
The sum of supplementary angles is \[180^\circ \]
So, the supplement of the angle is \[180^\circ - x\]
And from the information it is given that measure of an angle is 9 times its supplement
So, we have
 \[ \Rightarrow 9 \times ({180^o} - x) = x\]
On opening the bracket, we get
 \[ \Rightarrow x = {1620^{\text{o}}} - 9x\]
Now we will take 9x to the left side and add it to the x
 \[ \Rightarrow 10x = 1620\]
After this we will take 10 in the denominator of right, we will get
 \[ \Rightarrow x = \dfrac{{1620}}{{10}}\]
On division, we get
 \[ \Rightarrow x = 162^\circ \]

The measure of an angle which is 9 times its supplement is \[162^\circ \].

Note:
Supplement is what you subtract to the angle \[180^\circ \]. The angle which is remaining is the supplement angle. There are many types of angles in geometry like acute, obtuse, supplement. Angles which are smaller than \[90^\circ \] are acute angles. Angles which are larger than \[90^\circ \] are obtuse angles.