Question

Two complementary angles have measures of `3x -12°` and `x+30°`. What is the value of the smaller angle?

Answer 1

Value of smaller angle is `42^o`.

Explanation:

As the two angles `3x-12^o` and `x+30^o` are complementary they add up to `90^o`.

Hence `(3x-12^o)+(x+30^o)=90^o` or

`4x+18^o=90^o` or

`4x=90^o-18^o=72^o`

or `x=72^o/4=18^o`

Hence angles are `3xx18^o-12^o=54^o-12^o=42^o`

and `18^o +30^o=48^o`

and value of smaller angle is `42^o`.