Question

One acute angle and one obtuse angle can make pair of supplementary angle .Is this statement true?If not give reasone

Answer 1

Given,

Statement : One acute angle and one obtuse angle can make pair of supplementary angle.

To find,

The given statement is true or false.

Solution,

According to the geometrical definitions of acute angle, obtuse angle and supplementary pair of angle, we get the following information.

1. An acute angle is greater than 0° and less than 90°.
2. An obtuse angle is greater than 90° and less than 180°.
3. The sum of the two angles of a supplementary pair of angles, is 180°.

Now, we can take the following example,

Suppose there is an acute angle of value 60° and there is an obtuse angle of value 120°.

If we add the above mentioned two angles, then we will get,

= 60°+120°

= 180°

= Supplementary pair of angles (Information No.3)

[We can do the same proof with other values also, like (30°,150°),(80°,100°) etc.]

Hence, the given statement is true.