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

Below is an isosceles trapezoid.

B=2y+20 ∢B=2y+20

D=60 ∢D=60

Find B ∢B .

AAABBBDDDCCC2y+2060°

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's find the size of angle B.
00:11 We have an isosceles trapezoid. Let's explore the given information.
00:16 Remember, in a trapezoid, angles on the same leg add up to 180 degrees.
00:26 Now, let's substitute the given values to solve for Y.
00:40 Great! Let's isolate Y step-by-step.
00:54 And here is the value of Y.
01:00 Now, let's use this value to find angle B.
01:19 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Below is an isosceles trapezoid.

B=2y+20 ∢B=2y+20

D=60 ∢D=60

Find B ∢B .

AAABBBDDDCCC2y+2060°

2

Step-by-step solution

To answer the exercise, certain information is needed:

  1. In a quadrilateral the sum of the interior angles is 180.

  2. The isosceles trapezoid has equal angles.

  3. 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!

3

Final Answer

120°

Practice Quiz

Test your knowledge with interactive questions

True OR False:

In all isosceles trapezoids the base Angles are equal.

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