Can we have two acute angles whose sum is

(a) an acute angle? Why or why not?

(b) a right angle? Why or why not?

(c) an obtuse angle? Why or why not?

(d) a straight angle? Why or why not?

(e) a reflex angle? Why or why not?

(a) Yes, we can have two acute angles whose sum is an acute angle.

We know that,

Acute angle is one that measures between 0° and 90°.

So, suppose we have two acute angles 30° and 40° then, sum of these two would be 70° and this lies between 0° and 90° therefore 70° is also acute .

You can think of more such examples.

[Note: basically, when two consider two acute angles smaller than 45° then their sum would always be smaller than 90° and so angle obtained will be acute.]

(b) Yes, we can have two acute angles whose sum is a right angle.

Example: 30° + 60° = 90°

45° + 45° = 90°

(c) Yes, we can have two acute angles whose sum is an obtuse angle.

We know that,

Acute angle is one that measures between 0° and 90°.

And obtuse angle is one that measures between 90° and 180°.

So, suppose we have two acute angles 50° and 60° then, sum of these two would be 110° and this lies between 90° and 180° therefore 110° is an obtuse angle .

You can think of more such examples.

[Note: basically, when two consider two acute angles greater than 45° then their sum would always be greater than 90° and so angle obtained will be obtuse.]

(d) No, we can have two acute angles whose sum is a straight angle.

We know that,

Acute angle is one that measures between 0° and 90°.

And straight angle measures 180°

If we take two 90° angles then we can obtain a straight angle but 90° is not an acute angle. So, in any case we cannot obtain a straight angle using two acute angles.

[Note: measure of acute angle is always less than 90° and on adding two 90° angles we are obtaining a straight angle. So, if we add any other acute angles then their sum would always be less than 180°.]

(e) No, we can have two acute angles whose sum is a straight angle.

We know that,

Acute angle is one that measures between 0° and 90°.

And reflex angle measures between 180° and 360°

If we take two 90° angles then we can obtain a 180° angle but 90° is not an acute angle. So, in any case we cannot obtain an angle which is greater than 180° (or a reflex angle).

[Note: measure of acute angle is always less than 90° and on adding two 90° angles we are obtaining a straight angle. So, if we add any other acute angles then their sum would always be less than 180°.]