Question

Which of the following statements is true?
(1 Point)
Two acute angles can be complementary to each other
Two obtuse angles can be complementary to each other
Two right angles can be complementary to each other
One obtuse angle and one acute angle can be complementary to each other

Answer 1

Answer:

statement 1 is true

Step-by-step explanation:

because two obtuse angle would be greater than 90(statement 2)

and also same goes with two right angles (statement 3)and one obtuse (statement 4)

Answer 2

The true statement is : two acute angles can be complementary to each other.

• When the sum of two angles becomes 90°, then those two angles are considered as complementary angles.
• Now, an acute angle is less than 90°. So, it is possible for two acute angles to become complementary to each other.

Eg. 60° and 30° both are acute angles, and their sum is 90°, so they are complementary as well.

• Now, an obtuse angle is greater than 90°. So, it is impossible for two obtuse angles to become complementary to each other. (As, both addends are individually greater than 90°, so their sum will be way greater than 90°).
• Now, a right angle is equal to 90°. Sum of two right angles is 180°, which doesn't satisfy the requirements of being complementary angles.
• Now, an obtuse angle is already greater than 90°, so when it will be added with an acute angle, there will be no possibility to have 90° as the sum. That's why, one obtuse angle and one acute angle cannot be complementary to each other.