Isosceles Trapezoid Problem: Finding Angle B When B=3x and D=x

Question

In an isosceles trapezoid ABCD

$∢B=3x$

$∢D=x$

Calculate the size of angle $∢B$ .

00:00 Find angle B

00:03 Given an isosceles trapezoid

00:10 In a trapezoid, angles on the same leg sum to 180 degrees

00:17 Let's substitute appropriate values and solve for X

00:27 Let's isolate X

00:30 This is the value of X

00:36 Let's substitute this value to find angle B

00:47 And this is the solution to the problem

To answer the question, we must know an important rule about isosceles trapezoids:

The sum of the angles that define each of the trapezoidal sides (not the bases) is equal to 180

Therefore:

∢B+∢D=180

3X+X=180

4X=180

X=45

It's important to remember that this is still not the solution, because we were asked for angle B,

Therefore:

3*45 = 135

And this is the solution!

135°