anonymous
  • anonymous
In Kite ABCD, shown below, Angle A =7x-3, Angle B = 8x, and Angle C = 10x. What is the value of angle D?
Geometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Here is the diagram |dw:1450043564961:dw|
Directrix
  • Directrix
You'll need to know some properties of a kite to get started. I have attached two charts from this site: http://www.coolmath.com/reference/kites#The_sides_and_angles_of_a_kite
Directrix
  • Directrix
Read those.

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Directrix
  • Directrix
I cannot tell from the diagram which angles have measures 8x and 10x. |dw:1450045744545:dw|
Directrix
  • Directrix
There are 3 angles at vertex B. I do not know which one has measure 8x. If you clear up the diagram, then I can help.
anonymous
  • anonymous
Angle A (the whole angle) is equal to 7x-3, Angle B (The whole angle) is equal to 8x, and Angle C (The whole angle) is equal to 10x.
Directrix
  • Directrix
|dw:1450046046812:dw|
anonymous
  • anonymous
Basically, angle A is equal to angle BAD, B is equal to angle ABC, etc.
Directrix
  • Directrix
Are you given on your text diagram which pairs of sides of the kite are congruent? We need to know where they are so that we can find the one pair of congruent angles of the kite.
Directrix
  • Directrix
Here is an example of what I mean.
anonymous
  • anonymous
Yeah, side BC = CD, and side BA = AD
Directrix
  • Directrix
|dw:1450046473963:dw|
Directrix
  • Directrix
Which pair of angles would be congruent?
anonymous
  • anonymous
I think angles B and D.
Directrix
  • Directrix
Correct. Do you remember what the sum of the interior angles of a quadrilateral is? For a triangle, it would be 180 but for a quadrilateral the sum is greater than that.
anonymous
  • anonymous
360˚
Directrix
  • Directrix
Correct. Because angles B and D have the same measure, think of the mystery angle D as having measure the same as B which is 8x. That done, solve this equation for x: 7x - 3 + 8x + 10x + 8x = 360 |dw:1450046740214:dw|
anonymous
  • anonymous
Oh ok, thanks! So x = 11, and D = 88˚?
Directrix
  • Directrix
Post what you get for x, okay? Then, one more step and this problem will be solved.
Directrix
  • Directrix
Yes. That is what I got. Though not asked, we ended up with two angles of 88 and two others of 110 and 74. They sum to 360 as we knew they would.
anonymous
  • anonymous
Cool, thank you!
Directrix
  • Directrix
You are welcome.

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