Question

The difference in the measure of the two complementary angles is \[12^o\].Find the measures of the angle.

Answer 1

Hint: In this question, we need to find the measures of the angles. Two angles are said to be complementary angles if their sum is \[90^o\] . In some cases, they form a right angled triangle. Here We need to find the two complementary angles. Let us consider one angle be \[x^o\] and the other angle is \[x^o\] subtracted from \[90^o\] .

Complete answer:
We know that the two angles are said to be complementary, if the sum their measures is \[90^o\]
Let us consider the one angle be \[x^o\] and its complement be \[90^o – x^o\] (another angle)
Given, difference of \[x^o\] and \[90^o – x^o\] is \[12^o\]
\[x^o - \left( 90^o – x^o \right) = 12^o\]
By removing the parentheses,
We get,
\[x^o – 90^o + x^o = 12^o\]
By moving the constants to one side,
 \[2x^o = 12^o + 90^o\]
By adding,
We get,
\[2x^o = 102^o\]
\[x^o = \dfrac{102^o}{2}\]
By dividing,
We get,
\[x^o = 51^o\]
We have found the one angle i.e). \[51^o\]. Now we need to find the other angle.
It’s complement is \[90^o – x^o\]
W. K. T : \[x^o = 51^o\]
 \[90^o – 51^o\]
By subtracting,
We get,
 \[39^o\]
Thus the two complementary angles are \[51^o\]and \[39^o\]
Final answer :
The measures of the angle are \[51^o\ \] and \[39^o\].

Note:
Now we can verify the answer by subtracting the two complementary angles that we have found. If we get \[12^o\] by subtracting both the angles our answer is right. Examples for the complementary angles are \[60^o\] and \[30^o\] .Similarly, two angles are said to be supplementary angles if their sum is \[180^o\] . Example for supplementary angles are \[120^o\] and \[60^o \]