## FINDING THE MEASURE OF REFERENCE ANGLE

Finding the Measure of the Reference Angle :

Here we are going to see, how to find the measure of the reference angle.

Finding the Measure of the Reference Angle :

The reference angle is the acute angle formed between the terminal arm and the x-axis. The reference angle is always positive and measures between 0° and 90°.

## Finding the Measure of the Reference Angle - Examples

Question 1 :

What is the reference angle for each angle in standard position?

(a)   170°      (b)   345°     (c)   72°   (d)   215°

Solution :

(a) 170°

The reference angle of 170 is 190 - 170. That is 20°.

(b) 345°

The reference angle of 345 is 360 - 345. That is 15°.

(c)   72°

The reference angle of 72 is 90 - 72. That is 18°.

(d)   215°

The reference angle of 215 is 270 - 215. That is 55°.

## Finding Other Angles in Other Quadrant with Given Reference Angles

To determine the other angles in other quadrants, we have to use the following table.

The reference angle always be lesser than 90 degree.

Question 2 :

Determine the measure of the three other angles in standard position, 0° < θ < 360°, that have a reference angle of

(a) 45°       (b) 60°       (c) 30°       (d) 75°

Solution :

Let θ be given angle.

Required angle in 2nd quadrant  =  180 - θ

=  180 - 45  =  135

Required angle in 3rd quadrant  =  180 + θ

=  180 + 45  =  225

Required angle in 4th quadrant  =  360 - θ

=  360 - 45  =  315

Hence the required angles are 135, 225 and 315.

(b) 60°

Solution :

Let θ be given angle.

Required angle in 2nd quadrant  =  180 - θ

=  180 - 60  =  120

Required angle in 3rd quadrant  =  180 + θ

=  180 + 60  =  240

Required angle in 4th quadrant  =  360 - θ

=  360 - 60  =  300

Hence the required angles are 120, 240 and 300.

(c) 30°

Solution :

Let θ be given angle.

Required angle in 2nd quadrant  =  180 - θ

=  180 - 30  =  150

Required angle in 3rd quadrant  =  180 + θ

=  180 + 30  =  210

Required angle in 4th quadrant  =  360 - θ

=  360 - 30  =  330

Hence the required angles are 150, 210 and 330.

(d) 75°

Solution :

Let θ be given angle.

Required angle in 2nd quadrant  =  180 - θ

=  180 - 75  =  105

Required angle in 3rd quadrant  =  180 + θ

=  180 + 75  =  255

Required angle in 4th quadrant  =  360 - θ

=  360 - 75  =  285

Hence the required angles are 105, 255 and 285.

After having gone through the stuff given above, we hope that the students would have understood "Finding the Measure of the Reference Angle".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6