Question

Sketch each angle then find the measure of the reference angle for:A) -140 degreesB) 310 degree C) 115 degrees

Answer 1

The formula for reference angle formula is

The first angle is given below as

`=-140^0`

To figure out the quadrant under which it falls we will add 360 to it

`\begin{gathered} -140+360 \\ =220^0 \\ 220^0-180^0 \\ =40^0 \end{gathered}`

Hence,

-140 degrees fall under the THIRD QUADRANT as shown in the graph below

The reference angle for -140 degrees is

`\Rightarrow40^0`

Part B:

The angle given is

`310^0`

310 degrees fall under the 4th quadrant as shown in the image below

`\begin{gathered} 360^0-310^0 \\ =50^0 \end{gathered}`

The reference angle for 310 degrees

`\Rightarrow50^0`

Part C:

The angle given here is

`115^0`

The sketch is given below as

As the angle falls under the SECOND QUADRANT

The reference angle for 115 degrees is

`\Rightarrow65^0`