[tex]\rm\huge\pink{ANSWER}[/tex]
1. Given: Quadrilateral LEAF is a parallelogram.
a. If m∠L = x + 20 and m∠A = 2x – 12, what is m∠L?
STEP BY STEP SOLUTION:
To find m∠L, let's find first the x.
[tex]x+20=2x-12[/tex]
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Subtract 20 from both sides.
[tex]x+20-20=2x-12-20[/tex]
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Simplify.
[tex]x=2x-32[/tex]
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Subtract 2x from both sides.
[tex]x-2x=2x-32-2x[/tex]
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Simplify.
[tex]-x=-32[/tex]
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Divide both sides by –1.
[tex]\frac{-x}{-1}=\frac{-32}{-1}[/tex]
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Simplify.
[tex]x=32[/tex]
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Let the number x be 32.
m∠L = x + 20
m∠L = 32 + 20
m∠L = 52
Therefore, m∠L = 52°.
b. If LE = y + 14 and AF = 3y – 4, how long is AF?
STEP BY STEP SOLUTION:
To find how long AF is, let's find first the y.
[tex]y+14=3y-4[/tex]
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Subtract 14 from both sides.
[tex]y+14-14=3y-4-14[/tex]
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Simplify.
[tex]y=3y-18[/tex]
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Subtract 3y from both sides.
[tex]y-3y=3y-18-3y[/tex]
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Simplify.
[tex]-2y=-18[/tex]
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Divide both sides by –2.
[tex]\frac{-2y}{-2}=\frac{-18}{-2}[/tex]
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Simplify.
[tex]y=9[/tex]
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Let the number y be 9.
AF = 3y – 4
AF = 3(9) – 4
AF = 27 – 4
AF = 23
Therefore, AF = 23.
