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

Question

ABCD Deltoid.

Calculate the size of $∢D$ .

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

The side angles in a kite are equal, therefore:

$B=C=70$

Also, therefore:

$ACB=30$

$BCD=40$

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

$180-30-30=120$

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

$360-120-70-70=100$

$D=100$

100