The difference in the measures of two complementary angles is 12 degree .find the measures of the angles.

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Solution

Dear Student,

$I f t w o a n g l e s a r e c o m p l e m e n t a r y, t h e s u m o f t h e i r m e a s u r e s i s 90 ° L e t t h e o n e a n g l e b e x, t h e n t h e s e c o n d a n g l e w i l l b e 90 - x d e g r e e s B u t a c c o r d i n g t o q u e s t i o n, x - (90 - x) = 12 x - 90 + x = 12 2 x - 90 = 12 2 x = 12 + 90 2 x = 102 x = \frac{102}{2} = 51 ° S e c o n d a n g l e = 90 - 51 = 39 °$

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