Question

Consider the following statements:

Statement I: One of the supplementary angles is always an obtuse angle.

Statement II: One of the complementary angles is always an acute angle.

• A. Only Statement I is correct.
• B. Only Statement II is correct.
• C. Both the statements are corrent.
• D. None of the above.

Answer 1

The correct option is B Only Statement II is correct.

Supplementary angles are the angles whose measures when added equals ${180}^o.$

Consider two right angles:
${90}^o+{90}^o={180}^o$
$\therefore$ Two right angles are supplementary to each other.

However, ${90}^o$ is not obtuse neither acute.
Obtuse angle has a measure of more than ${90}^o,$ whereas acute angle has a measure of less than ${90}^o$.
$\therefore$ Statement I is wrong.

Complementary angles are the angles whose measures when added equals ${90}^o.$
Consider two angles: $a$ and $b$
$\to a+b={90}^o$
$\Rightarrow a={90}^o-b$
$\therefore$ Any of the angles should be less than ${90}^o.$

We can not say that both angles must be always acute angles.
$\because {90}^o+0^o={90}^o$
Here, $0^o$ is an acute angle and ${90}^o$ is a right angle.
$\therefore$ Statement II is correct.