Calculate Angle D in ABCD Deltoid: Given Angles 30° and 40°

ABCD Deltoid.

Calculate the size of ∢D ∢D .

AAABBBDDDCCC3040

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Step-by-step video solution

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00:00 Find angle D
00:07 Adjacent sides are equal in a kite
00:11 In an isosceles triangle, base angles are equal
00:23 The sum of angles in a triangle equals 180
00:33 Let's substitute appropriate values according to the given data
00:53 Let's collect terms and isolate D
01:13 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

ABCD Deltoid.

Calculate the size of ∢D ∢D .

AAABBBDDDCCC3040

2

Step-by-step solution

The side angles in a kite are equal, therefore:

B=C=70 B=C=70

Also, therefore:

ACB=30 ACB=30

BCD=40 BCD=40

Now we can calculate angle A. Since the sum of angles in a triangle is 180, this is done as follows:

180−30−30=120 180-30-30=120

Now we can calculate angle D. As we know, the sum of angles in a kite is 360, so:

360−120−70−70=100 360-120-70-70=100

D=100 D=100

3

Final Answer

100

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Indicates which angle is greater

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