beautiful_gurl
In parallelogram ABCD m<A is 30 more than m<B. Find the measure of m<D....
ALL WORK MUST BE SHOWN AND DIAGRAM NEEDED IF NECESSARY.
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LogicalApple
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What do we know about the angles in a parallelogram ? How are they related?
beautiful_gurl
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There equal?
LogicalApple
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Well, each angle has a corresponding angle on the opposite side, which is equal.
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So if the lower right angle is A = 30 + B then it would look like..
LogicalApple
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|dw:1357250721161:dw|
beautiful_gurl
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what?
LogicalApple
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The angle measurements
LogicalApple
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|dw:1357250780328:dw|
beautiful_gurl
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is it 30+B?
LogicalApple
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I think that is what you indicated in the question.
LogicalApple
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That angle A is 30 more than Angle B
beautiful_gurl
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okay
LogicalApple
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What I labeled in the diagram as "B" and "30 + B" are the angle measurements for each angle.
Last question is, what do the angle measurements add up to in a parallelogram ?
beautiful_gurl
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360?
LogicalApple
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Yes, exactly.
We can solve for B by adding up all the angles:
30 + B + B + 30 + B + B = 360
beautiful_gurl
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okay now what?
LogicalApple
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Solve for B and what do we get for the measure of angle B ?
beautiful_gurl
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how do I do that?
LogicalApple
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30 + 30 is 60, and B + B + B + B = 4B
so we have 60 + 4B = 360
beautiful_gurl
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now do you subtract 60 from 360?
LogicalApple
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Yes, that leaves
4B = 300
beautiful_gurl
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and then you divide by 4?
LogicalApple
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Precisely
beautiful_gurl
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and you get what?
LogicalApple
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B = 75 degrees
So we know that B = 75 degrees, and based on the parallelogram, would you agree that B = D ?
beautiful_gurl
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yes?
LogicalApple
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Then our conclusion is that the measure of angle D is 75 degrees :)
beautiful_gurl
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thanks
LogicalApple
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Sure np