Question

Q14. If the difference between two complementary angles is 10°, then the angles are: (a) 50°, 60° (b) 50°, 40° (c) 10°, 80° (d) 80°, 10°​

Answer 1

Answer:

option B.

Step-by-step explanation:

     Let those complementary angles be 'x' and 'y'.

We know that sum of complementary angles is 90°

                ∴ x + y = 90°         ...(1)

It is given that their difference is 10°.

                ∴ x - y = 10°          ...(2)

Adding (1) and (2), we get

     x + y = 90°

     x - y  = 10°  

   2x       = 100°  

           x = 50°

Substituting x in (1),   50° + y = 90°

                                ⇒ y = 40°

Therefore, the required angles are 50°, 40°

Answer 2

Question :-

Q14. If the difference between two complementary angles is 10°, then the angles are: (a) 50°, 60° (b) 50°, 40° (c) 10°, 80° (d) 80°, 10°.

Answer :-

• (b) 50°, 40°

Step by step explanation :-

Let,

• The complementary angles be x and y.

We know that,

Complementary angles are 90°.

Now, we have given that the difference between two complementary angles is 10°.

The equation becomes,

$\rm:\longmapsto{x + y = 90 \degree - - - (1)} \\ \\ \rm:\longmapsto{x - y = 10 \degree - - - (2)}$

On solving the equations, we get,

$\rm:\longmapsto{x + y + (x - y) = 90 + 10} \\ \\ \rm:\longmapsto{2x = 100 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \rm:\longmapsto{x = \frac{100}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{x = 50 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now, substituting x = 50 in equation (1)

$\rm:\longmapsto{50 + y = 90} \\ \\ \rm:\longmapsto{y = 90 - 50} \\ \\ \bf:\longmapsto \red{y = 40 \degree} \: \: \: \: \:$

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