the difference in the measure of two complementary angles is 12 find the measure of the angle
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the difference in the measure of two complementary angles is 12 find the measure of the angle
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Answer:
Hope this will help you
Step-by-step explanation:
Let one angle be x
Then,
Its complementary angle will be =(90-x)
ATQ,
x-(90-x)=12
x-90+x=12
x+x=12+90
2x=102
x=102/2
x=51
Thus,
x=51
(90-x)=(90-51)=39
Verified answer
Given :
To Find :
Solution :
Let,
The one angle be x.
The complement angle be 90° – x.
First, we need to find the value of x.
Given,
The difference between the measure of two complementary angles is 12°.
That means,
⇒ x – (90° – x) = 12°
⇒ x – 90° + x = 12°
⇒ x + x – 90° = 12°
⇒ 2x – 90° = 12°
⇒ 2x = 12° + 90°
⇒ 2x = 102°
⇒ x = 102° / 2
⇒ x = 51°
So, the measure of the angles are :
The one angle = x = 51°
The complement angle = 90° – x = 90° – 51° = 39°
Hence,
The measures of the two complementary angles are 51° and 39°.
Verification :
METHOD 1 :
The sum of the both angles is 90°
We have,
⇒ 51° + 39° = 90°
⇒ 90° = 90°
Hence Verified !
METHOD 2 :
The difference between the measures of both the angles is 12°.
We have,
⇒ 51° – 39° = 12°
⇒ 12° = 12°
Hence Verified !