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beautiful_gurl

  • 3 years ago

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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  1. LogicalApple
    • 3 years ago
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    What do we know about the angles in a parallelogram ? How are they related?

  2. beautiful_gurl
    • 3 years ago
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    There equal?

  3. LogicalApple
    • 3 years ago
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    Well, each angle has a corresponding angle on the opposite side, which is equal. |dw:1357250638700:dw| So if the lower right angle is A = 30 + B then it would look like..

  4. LogicalApple
    • 3 years ago
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    |dw:1357250721161:dw|

  5. beautiful_gurl
    • 3 years ago
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    what?

  6. LogicalApple
    • 3 years ago
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    The angle measurements

  7. LogicalApple
    • 3 years ago
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    |dw:1357250780328:dw|

  8. beautiful_gurl
    • 3 years ago
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    is it 30+B?

  9. LogicalApple
    • 3 years ago
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    I think that is what you indicated in the question.

  10. LogicalApple
    • 3 years ago
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    That angle A is 30 more than Angle B

  11. beautiful_gurl
    • 3 years ago
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    okay

  12. LogicalApple
    • 3 years ago
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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 ?

  13. beautiful_gurl
    • 3 years ago
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    360?

  14. LogicalApple
    • 3 years ago
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    Yes, exactly. We can solve for B by adding up all the angles: 30 + B + B + 30 + B + B = 360

  15. beautiful_gurl
    • 3 years ago
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    okay now what?

  16. LogicalApple
    • 3 years ago
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    Solve for B and what do we get for the measure of angle B ?

  17. beautiful_gurl
    • 3 years ago
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    how do I do that?

  18. LogicalApple
    • 3 years ago
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    30 + 30 is 60, and B + B + B + B = 4B so we have 60 + 4B = 360

  19. beautiful_gurl
    • 3 years ago
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    now do you subtract 60 from 360?

  20. LogicalApple
    • 3 years ago
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    Yes, that leaves 4B = 300

  21. beautiful_gurl
    • 3 years ago
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    and then you divide by 4?

  22. LogicalApple
    • 3 years ago
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    Precisely

  23. beautiful_gurl
    • 3 years ago
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    and you get what?

  24. LogicalApple
    • 3 years ago
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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 ?

  25. beautiful_gurl
    • 3 years ago
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    yes?

  26. LogicalApple
    • 3 years ago
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    Then our conclusion is that the measure of angle D is 75 degrees :)

  27. beautiful_gurl
    • 3 years ago
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    thanks

  28. LogicalApple
    • 3 years ago
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    Sure np

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