If (4x + 28) and (x - 8) are supplementary angles, find x.
(ii) An angle is 30° less than three times its complement. Find the angle.
Answers
Step-by-step explanation:
Solutions :-
i)
Given that
(4x+28)° and (x-8)° are Supplementary angles.
We know that
The sum of two angles is 180° are called Supplementary angles.
Therefore, (4x+28)° + (x-8)° = 180°
=> 4x+28°+x-8° = 180°
=> 5x+20° = 180°
=> 5x = 180°-20°
=> 5x = 160°
=> x = 160°/5
=> x = 32°
Therefore, x = 32°
The value of x = 32°
Check :-
We have, x = 32°
If x = 32° then 4x+28 = 4(32°)+28°
= 128°+28° = 156°
If x = 32° then x-8 = 32°-8° = 24°
The two angles are 156° and 24°
Sum of two angles = 156°+24° = 180°
They are Supplementary angles
Verified the given relations in the given
problem.
2)
Let the angle be X°
Then , it's complement = 90°-X°
According to the given problem
Angle = 3×Complement -30°
=> X° = 3(90°-X°)-30°
=> X° = 270°-3X°-30°
=> X° = 240°- 3X°
=> X° + 3X° = 240°
=> 4X° = 240°
=> X° = 240°/4
=> X° = 60°
Therefore, The angle is 60°
Check:-
The angle = 60°
It's complement = 90°-60° = 30°
Three times 30° = 3×30° = 90°
Now,
90°-30° = 60°
60° is 30° less than three times it's complement.
Verified the given relations in the given problem.
Solutions :
(¡) Complementary angle = 180°
so,
⇒ (4x + 28)° + (x - 8)° = 180°
⇒ 4x + x + 28 - 8 = 180
⇒ 5x + 20 = 180°
⇒ 5x = 160°
⇒ x = 32°
Angles are :
➻ (4x + 28)° = 128 + 28 = 156°
➻ (x - 8)° = 32 - 8 = 24°
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(¡¡) Let the angle be ‘ x ’ .
it's complement be (90 - x)
According to the Question,
Angle = 3(complement) - 30°
⇒ x° = 3(90 - x)° - 30°
⇒ x° = 270 - 3x° - 30°
⇒ 4x° = 240°
⇒ x° = 60°