The supplement of an angle and the complement of another have a sum equal to half of a complete angle. If the greater angle is 10° more than the smaller, then the measures of the angles are?
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Answers
Answer:
Thanks for the A2A.
This problem can be solved using any of the following methods:
Linear equations in one variable.
Linear equations in 2 variables.
Here I am solving it using the first method.
Let the angle be x
Then its complement = 90°-x
Thrice of it = 3x
Supplement of thrice = 180°–3x
Now, according to the question statement,
90°-x = 180°–3x
=> -x + 3x = 180°–90°
=> 2x = 90°
=> x = 45°
So the required angle is 45° .
Hope it helps.
Enjoy!
If an angle is 30 degree more than one half of its complement, than what is the measure of that angle?
The supplement of an angle is four times its complement. what is the angle?
What is the measure of an angle which is equal to its supplement?
The measure of an angle is 28° greater than its complement. How do you find the measure of each angle?
What is the measure of angle <ABC?
Let X be an angle, so thrice of it is 3X.
The complement of X = supplement of 3X.
two adjacent angles are called complementary if their sum is 90 degree, on the other hand, they will be called supplementary if the sum is 180 degree.
therefore,
90-X= 180–3X
3X-X=180–90
2X=90
x=45
So the angle is 45. Its complement is 45 and thrice the angle is 135, and the supplement of that is 45.
Complement of an angle, is it's adjacent angle in a right angle i.e (90 - that angle)
Supplement of an angle, is it's adjacent angle in a straight angle i.e (180 - that angle)
Let required angle be 'x'
Complement angle is c = 90 - x
Supplement of thrice the required angle is s = 180 - (3x)
It is given that s = c
Thus 90 - x = 180 - 3x
Adding 3x on both sides, and subtracting 90: 2x = 90
Dividing by 2 we get required angle.
x = 45°
The complement of an angle is 90 degrees minus the angle.
The supplement of an angle is 180 degrees minus the angle.
Thrice means times 3.
Let the angle be given the name N.
90 degrees minus N = 180 degrees minus three times N.
90 - N = 180 - 3 N
2 N = 90
N = 45
Check that a 45-degree angle is a correct answer.
The complement of 45 degrees is (90 - 45) degrees = 45 degrees.
Thrice 45 degrees = (3 * 45) degrees = 135 degrees.
The supplement of 135 degrees is (180 - 135) degrees = 45 degrees.
45 degrees is the correct answer.
So it's complementary angle is [math]90°-x°[/math]
And supplementary angle of thrice of [math]x°[/math] is [math]180°-3×x°[/math]
So [math]90°-x°=180°-3×x°[/math]
So [math]2×x°=90°[/math]
So angle under discussion is 45°, it's complementary angle is 45° and it's supplementary angle is 135°.
let us say the two angles are a and b,
a+b=90_________________(1)
also thrice of the angle is the supplement to the angle
3a+b=180_______________(2)
subtracting both equation we get,
2a=90
a=45
substituting the value of a in (1)
b=45
thus the two angles are 45° each
Let your angle be x
Complement of x is 90-x
By my understanding you mean supplement of of thrice the angle thus supplement of 3x which is equal to 180–3x
90–x=180–3x
x= 45° or π/4 radians
Let complement of an angle is n of an original angle (90-n). So supplement of that angle will be 180-90+n=90+n. So 3(90-n)=90+n, or 270-90=3n+n=4n. or n=180÷4=45°. So complent of the angle 45°=90-45=45° & complement of the angle =180-45=135°.
Ans:— 45° & 135°.
Let us assume the given angle be X
1.Now,complement of X will be equal to:
(90°-X)
Thrice of X is 3X
Supplement of thrice of X will be equal to:
(180°–3X)
Now,it says that (90-X)=(180°–3X)
-X+3X=180°–90°
2X=90°
X=45°
Assuming the angle to be ∅ its complement is 90-∅ and supplement as 180-∅. As per the relations between two=>(90-∅)=(180-∅)/3
=> 270–3∅=180-∅=>3∅-∅=270–180=90
=>2∅=90=>∅=(90/2)=45°.Ans..
If “x” is the angle, then its compliment of the angle= (90-x)
The supplement of the angle
= (180-x) .
So 3 (90- x)= (180- x)
So 2x= 90;
Therefore x= 45° .
So Angle=45°
Compliment Angle=45°
Supplement Angle= 135°
Let the angle be A.
Complement of A=90-A
Supplement of A = 180-A
It is given that 3(90-A) = 180-A
solving this equation we get , A=45.
Therefore the angles are 45 , 45.
Let the angle be x. According to the given condition, we get the equation
(90-x)=(180–3x)
Solve to get x=45°
Note that sum of complementary angles is 90° and that of supplementary angles is 180°
Hope that helped!
90-x = 180–3x
2x = 90
x = 45°
Let there is an angle of x° , its complement is (90°-x) and supplement of the thrice of it (180°-3x),
Acordingly:-
(90°-x)=(180–3x)
or. 90°-x=180–3x
or. 3x-x=180–90
or. 2x= 90. => x= 90°/2. = 45°.
Answer:
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