Suppose that angle LAP and angle LAR are adjacent angles, angle LAP= 3x +7, angle LAR = 4(x-4), And angle PAR = 2(3x+7). What can you conclude about line AL?

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luchoprat luchoprat · Answer 1 · 2019-09-15T03:24:46+02:00

Answer:

AL is a bisector

Step-by-step explanation:

LAP = 3x+ 7

LAR = 4(x - 4) = 4x - 16

PAR = 2(3x + 7) = 6x + 14

If you see the figure I drew (something you should infer from the problem.

LAP + LAR = PAR

3x + 7 + 4x - 16 = 6x + 14

3x + 4x - 6x = 14 + 16 - 7

x = 23

LAP = 3 * 23 + 7 = 76

LAR = 4 * 23 - 16 = 76

Meaning line AL is dividing PAR into 2 equal parts

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abidemiokin abidemiokin · Answer 2 · 2021-10-05T12:13:54+02:00

m<LAP = m<LAR, this means that the line AL bisects m<PAR

Find the diagram given,

[tex]m\angle LAP=3x + 7\\m\angle LAR=4(x-4)\\m\angle PAR=2(3x+7)[/tex]

The following expression is true;

[tex]m\angle LAR+m\angle LAP=m\anglePAR\\4x-16+3x+7=6x+14\\7x-9=6x+14\\7x-6x=14+9\\x=23\\\\[/tex]

Get the measure of m<LAR

m<LAR = 4x - 16

m<LAR = 4(23)-16

m<LAR=92-16

m<LAR= 76

Get the measure of m<LAP

m<LAP = 3x + 7

m<LAP = 3(23)+7

m<LAP=69+7

m<LAP=76

Since m<LAP = m<LAR, this means that the line AL bisects m<PAR

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