If two acute angles are added together, which of the following is NOT ...
An acute angle is less than 90°.
If you add two acute angles then
(i) the sum could be acute, example: 10° + 20° = 30° (an acute angle).
(ii) the sum could be right, example: 40° + 50° = 90° (a right angle).
(iii) the sum could be obtuse, example: 30° + 80° = 110° (an obtuse angle).
(iv) the sum could NOT be straight because each acute angle is less than 90° and a straight angle is 180°, example: 89° + 89° = 178° which is less than a straight angle.
View all questions of this test
If two acute angles are added together, which of the following is NOT ...
Explanation:
To understand why option 'D' (Straight) is not possible for the sum of two acute angles, let's first define the different types of angles mentioned in the question.
Acute Angle: An angle that measures less than 90 degrees.
Right Angle: An angle that measures exactly 90 degrees.
Obtuse Angle: An angle that measures between 90 and 180 degrees.
Straight Angle: An angle that measures exactly 180 degrees.
Now, let's consider the possible sums of two acute angles and see if they match the given options:
Sum of Two Acute Angles:
When we add two acute angles, the sum will always be less than 180 degrees because both angles are less than 90 degrees. Therefore, option 'A' (Acute) is possible for the sum of two acute angles.
Sum of an Acute Angle and a Right Angle:
When we add an acute angle (less than 90 degrees) and a right angle (90 degrees), the sum will be exactly 180 degrees. Therefore, option 'B' (Right) is possible for the sum of an acute angle and a right angle.
Sum of an Acute Angle and an Obtuse Angle:
When we add an acute angle (less than 90 degrees) and an obtuse angle (between 90 and 180 degrees), the sum will always be greater than 90 degrees but less than 270 degrees. Therefore, option 'C' (Obtuse) is possible for the sum of an acute angle and an obtuse angle.
Sum of Two Acute Angles:
Now, if we consider the sum of two acute angles, the maximum possible sum will be when both angles are 89 degrees. In this case, the sum will be 89 + 89 = 178 degrees, which is less than 180 degrees. Therefore, option 'D' (Straight) is NOT possible for the sum of two acute angles.
Hence, the correct answer is option 'D' (Straight).
To make sure you are not studying endlessly, EduRev has designed Class 5 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 5.