Question 169678This question is from textbook Geometry for enjoyment and challegne
: The measure of one angle of a parallelogram is 40 more than 3 times another. Find the measure of each angle.
This question is from textbook Geometry for enjoyment and challegne
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! in a parallelogram, the opposite angles are equal to each other.
the sum of the angles in a parallelogram is 360.
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if the parallelogram is labeled ABCD, then angle A is equal to angle C because they are opposite each other, and angle B is equal to angle D because they are opposite to each other.
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the labeling of the parallelogram would be:
A is lower left corner
B is upper left corner
C is upper right corner
D is lower right corner
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assume A and C are the smaller angles.
assume B and D are the larger angles.
the parallelogram will be tilting to the right so that corner B is to the right of corner A.
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problem states that the larger angle is 3 times the smaller angle plus 40 degrees.
since B is the larger angle and A is the smaller angle, that means that:
B = 3*A + 40
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since the sum of the angles in a parallelogram = 360 degrees then angle A + B + C + D = 360.
since angle A = angle C, and angle B = angle D, this can be rewritten as 2*A + 2*B = 360 degrees by substituting A for C and B for D.
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equation you start out with is:
2*A + 2*B = 360
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you know that B = 3*A + 40 so you can substitute in equation.
2*A + 2*B = 360 becomes:
2*A + 2*(3*A+40) = 360
simplify:
2*A + 2*3*A + 2*40 = 360
2*A + 6*A + 80 = 360
8*A + 80 = 360
subtract 80 from both sides of equation:
8*A = 360 - 80
8*A = 280
divide both sides of equation by 8:
A = 280 / 8
A = 35
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angle A is 35 degrees.
angle B is 3 * 35 + 40
angle B is 145 degrees.
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angle A and angle B = 180 degrees.
2 * angle A and 2 * angle B = 360 degrees.
this checks out with the sum of the angles of a parallelogram so the angles are good.
answer is:
smaller angle is 35 degrees.
larger angle is 145 degrees.
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