1.4 measure and classify angles
TRANSCRIPT
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Solve each equation.
1. 5x + 6 + 2x – 14 = 90
2. 4x – 30 + x + 25 = 180
ANSWER 14
ANSWER 37
ANSWER 10.5
3. + 2 = x – 5x3
1.4 Measure and Classify AnglesBell Thinger
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1.4Example 1
Name the three angles in the diagram.
You should not name any of these angles X because all three angles have X as their vertex.
WXY, or YXW
YXZ, or ZXY
WXZ, or ZXW
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a. KHJ b. GHK
Example 2
Use the diagram to find the measure of the indicated angle. Then classify the angle.
SOLUTION
A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.
a. HJ is lined up with the 0 on the inner scale of the protractor. HK passes through 55 on the inner scale. So, m KHJ = 55 . It is an acute angle.
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o
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a. KHJ b. GHK
Example 2
Use the diagram to find the measure of the indicated angle. Then classify the angle.
SOLUTION
b. HG is lined up with the 0 on the outer scale and HK passes through 125 on the outer scale. So, m GHK = 125 . It is an obtuse angle.
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1.4Guided Practice
1. Name all the angles in the diagram. Which angle is a right angle?
PQR , PQS, RQS ; PQS is a right angle .
ANSWER
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1.4Guided Practice
2. Draw a pair of opposite rays. What type of angle do the rays form?
ANSWER
Straight Angle
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1.4Example 3
ALGEBRA Given that m LKN =145 , find m LKM and m MKN.
o
SOLUTION
STEP 1
Write and solve an equation to find the value of x.
m LKN = m LKM + m MKN Angle Addition Postulate
Substitute angle measures.
145 = 6x + 7 Combine like terms.
Subtract 7 from each side.138 = 6x
145 = (2x + 10) + (4x – 3)o oo
23 = x Divide 6 from each side.
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1.4Example 3
ALGEBRA Given that m LKN =145 , find m LKM and m MKN.
o
SOLUTION
STEP 2
Evaluate the given expressions when x = 23.
So, m LKM = 56° and m MKN = 89°.ANSWER
CHECK
m LKN = m LKM + m MKN = 56° + 89° = 145°
m LKM = (2x + 10)° = (2 23 + 10)° = 56°
m MKN = (4x – 3)° = (4 23 – 3)° = 89°
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1.4Guided Practice
Find the indicated angle measures.
3. Given that KLM is a straight angle, find m KLN and m NLM.
ANSWER 125°, 55°
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1.4Example 4 The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m DEG = 157° ,what is m GKL?
Trapeze
SOLUTION There are two pairs of congruent angles:
DEF JKL and DEG GKL.~ ~
Because DEG GKL, DEG = m GKL.
So, m GKL = 157°.
~
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1.4Guided Practice
5. Identify all pairs of congruent angles in the diagram.
Use the diagram shown.
T and S, P and R.ANSWER
6. In the diagram, m PQR = 130 , m QRS = 84, and m TSR = 121 . Find the other angle measures in the diagram.
o
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o
m PTS = 121°, m QPT = 84°ANSWER
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1.4Example 5
SOLUTION
In the diagram at the right, YW bisects XYZ, and m XYW = 18 . Find m XYZ.
o
By the Angle Addition Postulate, m XYZ = m XYW + m WYZ. Because YW bisects XYZ you know that XYW WYZ. ~
So, m XYW = m WYZ, and you can write
m XYZ = m XYW + m WYZ = 18° + 18° = 36°.
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ANSWER right
ANSWER acute
ANSWER obtuse
Classify each angle as acute, obtuse , right and straight.
3. m C = 119 o
2. m B = 62 o
1. m A = 90
Exit Slip
ANSWER 14o
ANSWER 72o
4. If m DEG = 84 , Find m FEG.o
5. If XY bisects ZXW and m ZXY = 36 , find m ZXW.
o
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Homework
Pg 28-32#25, 40, 48, 51, 53