Question

This is my homework by the way.You can represent the measures of an angle and its complement as x° and (90 -x)° Similarly, you can represent the measures of an angle and its supplement as and (180 -- x)°. Use these expressions to find the measures of the angles described.The measure of an angle increased by 20° is equal to the measure of it's complement.

Answer 1

The measure of the angle is;

`35^(\circ)`

Step-by-step explanation:

Let x represent the angle.

The complement of angle x is;

`(90-x)^(\circ)`

If the measure of an angle increased by 20° is equal to the measure of it's complement.​ we have;

`x+20=90-x`

Let us solve the equation for x;

`\begin{gathered} x+20=90-x \\ \text{collect the like terms;} \\ x+x=90-20 \\ 2x=70 \\ x=(70)/(2) \\ x=35^(\circ) \end{gathered}`

Therefore, the measure of the angle is;

`35^(\circ)`