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

The correct option is B Only Statement II is correct.
Supplementary angles are the angles whose measures when added equals 180o.

Consider two right angles:
90o+90o=180o
Two right angles are supplementary to each other.

However, 90o is not obtuse neither acute.
Obtuse angle has a measure of more than 90o, whereas acute angle has a measure of less than 90o.
Statement I is wrong.

Complementary angles are the angles whose measures when added equals 90o.
Consider two angles: a and b
a+b=90o
a=90ob
Any of the angles should be less than 90o.

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

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