Question

The angles $ x-{{10}^{\circ }} $ and $ {{190}^{\circ }}-x $ are
A. interior angles on the same side of the transversal
B. making a linear pair
C. complementary
D. supplementary

Answer 1

Hint: We first explain the terms of the angles like complementary or supplementary angles. We need to find the sum of the angles which gives the sum being equal to either $ \pi $ or \[\dfrac{\pi }{2}\] making supplementary or complementary angles respectively.

Complete step-by-step answer:
If we take two angles $ x $ and $ y $ to find their sum, then the sum defines if the angles are complementary or supplementary angles.
If the sum is equal to $ \pi ={{180}^{\circ }} $ then the angles are supplementary angles to each other and if the sum is equal to \[\dfrac{\pi }{2}={{90}^{\circ }}\] then the angles are complementary angles to each other.
So, we have to find the sum of the given angles
 $ x-{{10}^{\circ }} $ and $ {{190}^{\circ }}-x $ .
The sum will be
\[\left( x-{{10}^{\circ }} \right)+\left( {{190}^{\circ }}-x \right)\].
Simplifying we get
\[x-{{10}^{\circ }}+{{190}^{\circ }}-x={{180}^{\circ }}=\pi \].
Therefore, the angles $ x-{{10}^{\circ }} $ and $ {{190}^{\circ }}-x $ are supplementary angles to each other.
So, the correct answer is “Option D”.

Note: Also, we need to remember that if the angles are the parts of a transversal, then the angles will be on the opposite sides of the transversal, not on the same side.