angle...angle relationships read & understand (highlight or circle important keywords.) a...

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©Exceeding the CORE Question # 0

PROBLEM SOLVING

GRAPHIC ORGANIZER

ANGLE

Adjacent Angles

Vertical Angles

Complementary Angles

Supplementary Angles

Relationships

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ANGLE RELATIONSHIPS

READ & UNDERSTAND (Highlight or circle

important keywords.)

In the figure below, the measures of ∠ABC is 58°and the measure of ∠DBE is 103°. Write and solve an equation to find ∠ABE.

What do we know? (List the important facts

needed for this problem to be solved.) _________________________________________________________________________________________________________ ___________________________________ What do we want to find out? (Explain in

your own words.) _________________________________________________________________________________________________________ ___________________________________

SOLVE (Answer the problem. Show all work.)

EXPLAIN (State your answer. Give details. Explain what you did and justify your steps.)

________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

B

● C

● A

● E

● D

● F

58°

103°

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ANGLE RELATIONSHIPS



What is the measure of the angle given by the opening of the scissors?



your own words.) _________________________________________________________________________________________________________ ___________________________________


EXPLAIN (State your answer. Give details. Explain what you did and justify your steps.) ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

(2x)°

112°

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ANGLE RELATIONSHIPS



Angles P and Q are complementary angles. The measure of ∠Q is (𝟔𝒙 + 𝟏)° , and the measure of ∠P is 29°. What is the value of 𝒙?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________


ANGLE RELATIONSHIPS



When a soccer ball hits a hard, level surface it bounces off at the same angle at which its hits. Use the figure below to find the angle at which the soccer ball hits the floor.



your own words.) _________________________________________________________________________________________________________ ___________________________________



x x 88°

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ANGLE RELATIONSHIPS



Angles A and B are supplementary.

If the measure of ∠𝑨 = 𝒙 − 𝟏𝟎 and the

measure of ∠𝑩 = 𝒙 + 𝟒, find the measure

of each angle.



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________


ANGLE RELATIONSHIPS



A pair of skis form vertical angles when they are crossed. Write and solve an equation to find the value of 𝒙.



your own words.) _________________________________________________________________________________________________________ ___________________________________



(x+2)° 43°

Name (s) __________________________________ Class__________ Date_________________________


ANGLE RELATIONSHIPS



A skateboard ramp makes an angle of

21° with respect to the ground as

shown below. How are the 21° angle

and the unknown angle related?

What is the value of 𝒙?


needed for this problem to be solved.) _________________________________________________________________________________________________________ ___________________________________

What do we want to find out? (Explain in

your own words.) _________________________________________________________________________________________________________ ___________________________________



(𝑥 + 5)° 21°

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ANGLE RELATIONSHIPS



Two angles are complementary. The

measure of the larger angle is 5 times

the measure of the smaller angle.

What are the measures of the

angles?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________


ANGLE RELATIONSHIPS



The measures of two supplementary

angles have a ratio of 2:3. What is

the measure of the larger angle?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________


ANGLE RELATIONSHIPS



The figure shows the intersection of Ocean Avenue, Farragut Road and Bedford Street. Find measure of ∠1, ∠2 and ∠3.



your own words.) _________________________________________________________________________________________________________ ___________________________________



Ocean Ave.

Farragut Rd.

Bedford St.

1 2

3 47°

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ANGLE RELATIONSHIPS PROBLEM SOLVING Answer Key

Answer Sample Work

1. The measure of ∠ABE is 78°. 𝑥 + 102 = 180; 𝑥 = 78

2. The measure of the angle given by the

opening of the scissors is 68°.

2𝑥 + 112 = 180 2𝑥 = 68 𝑥 = 34

3. The value of x is 10. 6𝑥 + 1 + 29 = 90 6𝑥 + 30 = 90 6𝑥 = 60 𝑥 = 10

4. The soccer ball hits the floor at a 46° angle. 𝑥 + 𝑥 + 88 = 180 2𝑥 + 88 = 180 2𝑥 = 92 𝑥 = 46

5. The measure of ∠𝐴 is 83° and the measure of ∠𝐵 is 97°.

𝑥 − 10 + 𝑥 + 4 = 180 2𝑥 − 6 = 180 2𝑥 = 186 𝑥 = 93 ∠𝐴 = 93 − 10 = 83 ∠𝐵 = 93 + 4 = 97

6. The value of x is 41°

𝑥 + 2 = 43 𝑥 = 41

7. The angles are supplementary. The value of x is 154°.

𝑥 + 5 + 21 = 180 𝑥 + 26 = 180 𝑥 = 154

8. The measures of the angles are 15° and 75°. 𝑥 + 5𝑥 = 90 6𝑥 = 90 𝑥 = 15 5𝑥 = 75

9. The measure of the larger angle is 108°. 2𝑥 + 3𝑥 = 180 5𝑥 = 180 𝑥 = 36 𝑙𝑎𝑟𝑔𝑒𝑟 𝑎𝑛𝑔𝑙𝑒 = 3𝑥 = 108

10. The measure of ∠1 is 133°. The measure of ∠2 is 47° and the measure of ∠3 is 43°.

𝑚∠1 47 + 𝑥 = 180; 𝑥 = 133 𝑚∠2 133 + 𝑥 = 180; 𝑥 = 47 𝑚∠3 47 + 𝑥 = 90; 𝑥 = 43

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