Question

Supplementary angle of angle $\angle A$ is angle $\angle B.$ Measure of any of the angles $\ne 0$. Choose the option which is/are always true.

• A. A: Acute angle
  B: Obtuse angle
• B. A: Acute angle
  B: Acute angle
• C. A: Obtuse angle
  B: Obtuse angle
• D. A: Obtuse angle
  B: Acute angle

Answer 1

Answer: (A), (D)

A: Obtuse angle

B: Acute angle
$\angle A$ and $\angle B$ are supplementary angles.

$\therefore \angle A+\angle B={180}^o$
$\Rightarrow \angle A={180}^o-\angle B$

Given: Measure of any of the angles $\ne 0$.
For $\angle B$ as an acute angle, $\angle A$ is always an obtuse angle.

Example: Let $\angle B={30}^o.$
$\therefore \angle A={180}^o-\angle B={180}^o-{30}^o={150}^o$
${150}^o$ is an obtuse angle.

Similarly, for $\angle B$ as an obtuse angle $(={130}^o),$ $\angle A={50}^o,$ which is an acute angle.

Hence, options (a) and (d) are correct.