Question

The difference in the measures of two complementary angles in 12 degrees. Find the measures of the angles.

Answer 1

${ \red{ \huge{ \bold{ \underline{ \: QUESTION }}}}}$

▪ The difference in the measure of two complementary angles is 12 degrees . Find the measures of the angles.

${ \red{ \huge{ \bold{ \underline{ \: </strong><strong>SOLUTION</strong><strong> </strong><strong>}}}}}$

Let the two complementary angles be x° and y° respectively .

Assume that angle x is greater than angle y...

¤ Complementary angles:-

----> two angles are said to be complementary if their sum is equal to 90°

thus, it can be represented in the form of equation as,

x° + y° = 90° ----------------> eqn ( 1 )

according to the question,,

the difference between the measure of these two angles is 12°

thus,

x° - y° = 12° ------------------> eqn ( 2 )

=》it can be seen that these two equations are in the form of simultaneous equation in two variables.....

adding equations (1 ) and ( 2).......

( x° + y°) + ( x° - y° ) = 90° + 12°

=》 x° + x° + y° - y° = 102°

=》 2x° = 102°

=》 x° = 51°

¤ Substituting the value of x in equation ( 1 )

x° + y° = 90°

=》51° + y° = 90 °

=》y° = 90° - 51°

=》y° = 39°

☆☆ therefore,

the two complementary angles are 39° and 51°.

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