the difference in the measures of two complementary angles is 12°. Find the measures of the angles
Answers
Let one angle be x
then other angle be x-12°
given that they are complementary,
x+(x-12°)=90°
2x=90°+12°
2x=102°
x=51°
x-12°=51°-12°=39°
∴The two complementary angles are of 39° and 51°
Complementary Angles:
Definition: A pair of angles which sums up to 90° are called complementary angles and one angle is said to be a complement of the other.
Uses: Used for finding properties of various polygons.
Example: 30°, 60° [30+60 = 90°].
Method 1:
So, coming to the question, we have been given the difference between 2 complementary angles and are supposed to find their sum.
Let the larger angle be denoted by the variable x and the smaller angle be denoted by the variable y.
Now, we have to form 2 linear equations in 2 variables.
Equation 1:
x + y = 90.
Equation 2:
x - y = 12.
Adding equation 1 and equation 2:
(x + y) + (x - y) = 90+12.
2x = 102.
x = 102/2
x = 51°.
Substituting the value of x in equation 2:
(51) - y = 12
- y = 12-51
- y = - 39
y = 39°.
Method 2:
This can also be solved using linear equation in 1 variable where x is the larger angle and the smaller angle is x-12.
We know that their sum is 90°.
(x) + (x - 12) = 90.
2x = 102.
x = 51°
x - 12 = 51 - 12 = 39°
Therefore, the 2 complementary angles are 51° and 39°.