Question

Two complementary angles differ by 12° then the
angles are
A) 53°, 41° B) 51°, 39° C) 54°, 42° D) 52°, 40°
Ο Α
OB
Ос
OD​

Answer 1

• Option (B) 51°, 39° is correct.

Given :–

• Two complementary angles differ by 12°.

To Find :–

• The angles.

Solution :–

Let,

The first angle be x.

We know that,

Sum of two complementary angles = 90°.

That means,

The second angle be 90° – x.

According to the condition,

Difference between both angles is 12°.

I.e.,

• First angle – Second angle = 12°

So,

$\longmapsto x - (90 \degree - x) = 12 \degree$

Now, open the bracket.

$\longmapsto x - 90 \degree + x = 12 \degree$

$\longmapsto x + x - 90 \degree = 12 \degree$

$\longmapsto2x - 90 \degree = 12 \degree$

$\longmapsto2x = 12 \degree + 90 \degree$

$\longmapsto2x = 102 \degree$

$\longmapsto x = \cancel \dfrac{102 \degree}{2}$

$\longmapsto x = 51 \degree$

So,

The first angle = x = 51°

The second angle = 90° – x = 90° – 51° = 39°

Hence,

The first angle is 51° and the second angle is 39°.

So, the option (B) is correct.

Verification :–

Substitute the both angles in equation (1),

$\longmapsto x - (90 \degree - x) = 12 \degree$

Here the values are,

• x = 51°
• 90° – x = 39°
• Difference between both the angles = 12°

$\longmapsto 51 \degree - 39 \degree = 12 \degree$

$\longmapsto12 \degree = 12 \degree$

Hence Verified !!

Answer 2

Answer:

I think O B is the answer of questions

Step-by-step explanation:

the sum of complementary angles =90°

90-51 gives us 39° and difference between the both is 12°