Question

supplement of an angle is 30 degree less than 4 times its complement find the angle​ solve with explanation please

Answer 1

Step-by-step explanation:

Since we have that the supplement is 30 more than 4 times the complement, then 180 - x = 4(90 - x) + 30. We have to multiply the compliment by 4 and then add 30 to it to get the supplement. 180 - x = 4(90 - x) + 30

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Answer 2

Step-by-step explanation:

Given :-

Supplement of an angle is 30 degree less than 4 times its complement .

To find :-

Find the angle ?

Solution :-

Let the angle be X°

Then,

Complementary angle of X° = (90-X)°

4 times the complementary angle = 4(90-X)°

and,

The supplementary angle of X° = (180-X)°

According to the given problem

Supplementary angle = 30° less than 4 times it's Complementary angle.

=> (180-X)° = 4(90-X)° -30°

=> 180° - X° = 360° - 4X° -30°

=> 180° -X° = 330° -4X°

=> -X° + 4X° = 330° -180°

=> 3X° = 150°

=> X ° = 150°/3

=> X° = 50°

Therefore, X° = 50°

Answer:-

The required angle for the given problem is 50°

Check:-

The angle = 50°

It's Complementary angle = 90°-50° = 40°

It's Supplementary angle = 180°-50° = 130°

=> 130° = 160°-30°

=> 130° = 4×40° -30°

=> 130° = 4×Complementary angle -30°

supplement of an angle is 30 degree less than 4 times its complement .

Verified the given relations in the given problem.

Used formulae:-

• Complementary angle of X° = (90-X)°

• Supplementary angle of X° = (180-X)°

Points to know:-

Complementary angles :

The sum of two angles is equal to 90° .They are called Complementary angles.

Supplementary angles :

The sum of two angles is equal to 180° .They are called Supplementary angles.