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

Question

ABCD Deltoid.

Calculate the size D ∢D

AAABBBDDDCCC3040

Video Solution

Step-by-Step Solution

We know that in a kite, the side angles are equal to each other, meaning:

B=C=70 B=C=70

And therefore also:

ACB=30 ACB=30

BCD=40 BCD=40

Now we can calculate angle A. As we know, the sum of angles in a triangle is 180, so:

1803030=120 180-30-30=120

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

3601207070=100 360-120-70-70=100

D=100 D=100

Answer

100