Question

A) an Angle measures 42° what is the measure of the supplement?B) an Angle measures 61°what is the measure of its complement?

Answer 1

Two angles are supplementary if the sum of their measures is equal to 180°. In part A we are told that an angle measures 42° and we have to find its supplement. Using what I stated before, the measure of the supplement (x) plus 42° must be equal to 180°:

`180^(\circ)=42^(\circ)+x`

We can substract 42° from both sides:

`\begin{gathered} 180^(\circ)-42^(\circ)=42^(\circ)+x-42^(\circ) \\ 138^(\circ)=x \end{gathered}`

So the answer to part A is 138°.

Two angles are complementary if the sum of their measures is equal to 90°. In part B we have to find the measure of the complement (y) of 61°. Following the definition of complementary angles the sum of y and 61° is equal to 90° then:

`y+61^(\circ)=90^(\circ)`

We can substract 61° from both sides:

`\begin{gathered} y+61^(\circ)-61^(\circ)=90^(\circ)-61^(\circ) \\ y=29^(\circ) \end{gathered}`

Then the answer to part B is 29°.