Calculate the Fourth Angle in a Trapezoid: Given Angles 110°, 130°, and 70°

Question

ABCD is a trapezoid.

$∢A=110$

$∢B=130$

$∢C=70$

Calculate the size of angle $∢D$ .

00:00 Find angle D

00:12 The sum of adjacent angles in a trapezoid is always equal to 180

00:26 Substitute appropriate values according to the given data

00:35 Isolate angle D

00:48 And this is the solution to the question

The sum of angles in a trapezoid is 360 degrees.

Therefore:

$360=A+B+C+D$

Let's substitute the known data into the above formula:

$360=110+130+70+D$

$360=310+D$

We'll move terms and maintain the appropriate sign:

$360-310=D$

$50=D$