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

Solution:

The formula for reference angle formula is

The first angle is given below as

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

Hence,

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

The reference angle for -140 degrees is

Part B:

The angle given is

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

The reference angle for 310 degrees

Part C:

The angle given here is

The sketch is given below as

As the angle falls under the SECOND QUADRANT

The reference angle for 115 degrees is

Ihad to look for the figure and here is my answer:

based on the given circle d with angles adc and arc ac, here is how we are going to look for the measure of angle abc:
arc ac=angle adc
8x-8=7x+2
8x-7x=2+8
x=10
< adc=7(10)+2=72
< abc=72/2=36
so the answer for this is 36 degrees.