Find Angle B = 2y+20 in an Isosceles Trapezoid with 60° Angle

Question

Below is an isosceles trapezoid.

$∢B=2y+20$

$∢D=60$

Find $∢B$ .

00:00 Find Y

00:03 An isosceles trapezoid according to the given data

00:08 In a trapezoid, angles on the same leg sum to 180

00:18 Let's substitute appropriate values and solve for Y

00:32 Let's isolate Y

00:46 This is the value of Y

00:52 Let's substitute this value to find angle B

01:11 And this is the solution to the problem

To answer the exercise, certain information is needed:

In a quadrilateral the sum of the interior angles is 180.
The isosceles trapezoid has equal angles.
From here it is we know that the sum of the angles adjacent to a side of the trapezoid is 180°.

We turn this conclusion into an exercise:

2y+20+60=180

We add up the relevant angles

2y+80=180

We move the sections:

2y=180-80

2y=100

Divided by 2

y=50

When we substitute Y we get:

2(50)+20=120

And this is the solution!

120°