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Question
AnswersState whether the given statement is true or false:
The measure of an obtuse angle is less than ${90^ \circ }.$
Answer
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Hint: Obtuse angle is always greater than ${90^ \circ }$
From the definition of obtuse angle, we know that its value lies between ${90^ \circ }$and ${180^ \circ }$(both excluding) i.e.,
${90^ \circ } < $ obtuse angle $ < {180^ \circ }$
Therefore, the given statement is false.
Note: Angles are divided into three categories on the basis of their measurement. Acute angle, obtuse angle and right angle. The measure of right angle is ${90^ \circ }$ while the measure of acute angle is always less than ${90^ \circ }$.
From the definition of obtuse angle, we know that its value lies between ${90^ \circ }$and ${180^ \circ }$(both excluding) i.e.,
${90^ \circ } < $ obtuse angle $ < {180^ \circ }$
Therefore, the given statement is false.
Note: Angles are divided into three categories on the basis of their measurement. Acute angle, obtuse angle and right angle. The measure of right angle is ${90^ \circ }$ while the measure of acute angle is always less than ${90^ \circ }$.