Question

5.
5. Two complementary angles differ by 24°,
then larger angle is......?
Full Marks : 1
a) 52°
b) 28°
C) 50°
d) None of these
6.​

Answer 1

Step-by-step explanation:

If two angles are complementary, the sum of their measures is 90 degrees.

Let one angle be x.

This means that its complement is 90−x degrees.

But the difference in their measures is 12 degrees.

Therefore, you can write the equation:

x−(90−x)=12

Since the parentheses are preceded by a minus sign, you can remove the parentheses if you also change the signs of the terms inside the parentheses. Therefore, when you remove the parentheses

the equation becomes:

x−90+x=12

Combine the two x terms on the left side to get:

2x−90=12

Get rid of the −90 on the left side by adding 90 to both sides to get

2x=102

Solve for x by dividing both sides of the equation by 2 to get:

x=

2

102

=51

Answer 2

Answer: D) None of these.

Step-by-step explanation:

As we know the difference it is easy to find the larger angle.

A complementary angle always adds up to 90 degree.

So let us take their value as x and y.

We know that their difference is 24, so x - y = 24.

We also know that their sum is 90, so x + y = 90.

Now to get the larger angle, We will ADD the sum and the difference.

So, x + y + x - y = 24+90

 2x = 114  (+y and -y will get cancelled; they are equal to zero)

 x = 114/2

   = 57 degree

So the correct option is D) None of these.

Hope this helps you.

Thank you.