1. How to Find Unknown Angles

2. How to Find Unknown Angles
example 1
84 x
Find the m x
1st: think of what you know or what the problem tells you
-the two angles are a linear pair (form a straight line together), so they must add to = 180°.
2nd: write an equation based on what you know
x + 84 = 180
3rd: solve the equation
-84 = -84
x = 96
4th: answer the question
the missing angle is  x = 96
Missing angle is 96°

3. How to Find Unknown Angles
example 2 J
Find the measure of each unknown angle O
4x° x° K M
1st: think of what you know or what the problem tells you
-since the index (box in the corner of the angle) tells us that <JKM is right, it must = 90°.
-the 4x angle and the x angles must be complementary and add together to 90°
2nd: write an equation based on what you know
4x + x = 90
3rd: solve the equation
5x = 90
x = 18
4th: answer the question
the missing angles were x and 4x, so plug 18 back in as x and simplify them both x=18, and 4(18)=72
Missing angles are 18° and 72°

4. How to Find Unknown Angles
example 3 D F E H
3x x
Find the measure of each unknown angle
1st: think of what you know or what the problem tells you
-the two angles are a linear pair (form a straight line together), so they must add to = 180°.
2nd: write an equation based on what you know
x + 3x = 180
3rd: solve the equation
4x = 180
x = 45
4th: answer the question
the missing angles were x and 3x, so plug 45 back in as x and simplify them both x=45, and 3(45)=135
Missing angles are 45° and 135°

5. How to Find Unknown Angles
example 4
m 4 = 2x +5
m 5 = x + 30
Find the m 4 and m 6 4 5 6
1st: think of what you know or what the problem tells you
-  4 and 5 are vertical angles, so they are congruent (= measure)
-  4 and 6 are supp. / form a linear pair (form a straight line), so they must add to = 180°.
2nd: write an equation based on what you know
 4 =  5 so
2x + 5 = x + 30
3rd: solve the equation
x + 5 = 30
x = 25
4th: answer the question
plug 25 back in as x to find missing angles
 4 = 2x + 5
 4 = 2(25) + 5
 4 = 55 and also  4 +  6 = 180, so  6 = 125
Missing angles are  4=55° and  6=125°

6. How to Find Unknown Angles
example 5
Try one if you are only given a description!
Angle a and angle b are supplementary angles.
If angle a is one-fifth the measure of b, what is the measure of each angle?
Draw your own diagram!
1st: think of what you know
Since <a and <b are supplementary, they must add to 180°.
If <a is unknown, call it x.
If <a is one-fifth of <b, then <b must be 5x because it will be 5 times bigger.
2nd: write an equation
x + 5x = 180
3rd: solve the equation
6x = 180
x = 30
4th: answer the question
<a = 30° and <b = 150° a b x 5x