Quadrilaterals and Polygons: Parallelograms

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Define parallel lines.
 

Parallel lines are lines that are coplanar and never cross.
 

Angle A and angle B are supplementary. Angle A measures (3x + 5)° and angle B measures (2x – 10)°. Find the measure of each angle.
 

(3x + 5) + (2x – 10) = 180
x = 37 insert image: measure of angle A = [3(37) + 5]° = 116°
insert image: measure of angle B= [2(37) – 10]° = 64°
 

Solve this system of equations:
8x + 9y + 4x + 15 = 180
10y + 5 = 4x + 15
 
12x + 9y = 165
3(-4x + 10y = 10)

12x + 9y = 165
-12x + 30y = 30

39y = 195
y = 5

12x + 9(5) = 165
12x = 120
x = 10

x = 10, y = 5
 

If lines 1 and 2 are parallel, what can you say about angle A and angle B?

parallel lines 1 and 2 cut by a transversal, the angle below the top line and to the left of the transversal is A, the angle above the bottom line and to the left of the transversal is B.
 

Angle A and angle B are supplementary; they add up to 180°.


 

If line 1 and 2 are parallel, find the value of a.

parallel lines 1 and 2 cut by a transversal, the angle below the top line and to the left of the transversal is 2 a minus 6 degrees, the angle above the bottom line and to the left of the transversal is 3 a plus 21 degrees.

(2a – 6) + (3a + 21) = 180
a = 33