Q. 745.0( 2 Votes )

Can we have two a

Answer :

(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°.]


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