Question

Difference between two complementary angles
is 60°. Find each angle.​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

What is complementary angles ?

Complimentary angles are pair of those angles whose sum makes an angle of 90°.

Now ,taking various cases to find out the angle measure.

Given that the difference of two complementary angles is 60°

Let us assume that the first angle be x

second angle be y

According to the Question

x-y=60°

Taking possible cases

90°30°=60° case I

Here ,it is not possible because 90+30=120>90° which not formed a complimentary angle.

Taking 2nd situation

80-°20°=60° Case II

Here,it's not possible because 80°+20°=100° which is >90° not a complimentary angle.

70-10°=60° Case III

It is possible because 70+10=80° which is <90° it's also not a complimentary angle

Case IV

75°-15°= 60°

Here,it's a complimentary angles pair

as 75°+15°=90°

∴The angles are 75° & 15°

Alternative method

Let the first angle be 'x'

second angle be 90-x

90-x-x=60°

90-2x=60

-2x=-30

x=15

second angle =90-15=75°

∴The angles are 15° & 75°

Answer 2

Answer:

What is complementary angles ?

Complimentary angles are pair of those angles whose sum makes an angle of 90°.

Now ,taking various cases to find out the angle measure.

Given that the difference of two complementary angles is 60°

Let us assume that the first angle be x

second angle be y

According to the Question

x-y=60°

Taking possible cases

90°30°=60° case I

Here ,it is not possible because 90+30=120>90° which not formed a complimentary angle.

Taking 2nd situation

80-°20°=60° Case II

Here,it's not possible because 80°+20°=100° which is >90° not a complimentary angle.

70-10°=60° Case III

It is possible because 70+10=80° which is <90° it's also not a complimentary angle

Case IV

75°-15°= 60°

Here,it's a complimentary angles pair

as 75°+15°=90°

∴The angles are 75° & 15°

Alternative method

Let the first angle be 'x'

second angle be 90-x

90-x-x=60°

90-2x=60

-2x=-30

x=15

second angle =90-15=75°

∴The angles are 15° & 75°

hope it is helpful thank you