Question

Which of the following statements is always true about lines and angles?

• A. Sum of complementary angles $={90}^o$
• B. Sum of supplementary angles $={90}^o$
• C. Vertical angles supplement each other
• D. Sum of vertical angles $={90}^o$

Answer 1

The correct option is A Sum of complementary angles $={90}^o$

Detailed step-by-step solution:
Let’s consider all the three types of angles mentioned here.
Vertical angles: When two straight lines intersect each other at one point, the opposite angles are called vertical angles.


You will get equal vertical angles. The actual measurement of these vertical angles will depend on the direction of each of the lines intersecting.
In the above figure, $\angle A=\angle C={62}^O$ and $\angle B=\angle D={118}^O$.
Vertical angles are supplementary angles only if their measurements are ${90}^O$.
And vertical angles are complementary angles only if their measurements are ${45}^O$.
$\to$ So, options A and C are not always true.

Supplementary angles: If the sum of two angles is ${180}^0$, then one angle is supplementary to another.


Here, ${130}^o$ is a supplementary angle of ${50}^o$, and ${50}^o$ is a supplementary angle of ${130}^o$.
$\to$ So, option B is not true.

Complementary angles: If the sum of two angles is ${90}^o$, then one angle is complementary to another.


Here, ${30}^o$ is a complementary angle of ${60}^o$, and ${60}^o$ is a complementary angle of ${30}^o$