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

Q: Why do angles B and D add up to 180° if they're not next to each other?

Great observation! In an isosceles trapezoid, angles B and D are actually adjacent to the same parallel side. Think of them as "co-interior" angles, which always sum to 180°.

Q: How do I know which angles are equal in an isosceles trapezoid?

In an isosceles trapezoid, base angles are equal. So angle A = angle B, and angle C = angle D. The diagram shows this isn't the case here, so we use the supplementary property instead.

Q: What if I get a negative value for y?

Check your algebra! In this problem, $ 2y = 100 $, so y should be positive. Negative angles don't make sense in geometry, so review your equation setup.

Q: How do I remember which angles are supplementary in a trapezoid?

Think of it this way: angles on the same side of the trapezoid (like B and D in this problem) always add to 180°. This is true for any trapezoid, not just isosceles ones!

Isosceles Trapezoid Angles with Algebraic Expressions

Below is an isosceles trapezoid.

$∢B=2y+20$

$∢D=60$

Find $∢B$ .

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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

Understand the problem

Below is an isosceles trapezoid.

$∢B=2y+20$

$∢D=60$

Find $∢B$ .

Step-by-step solution

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!

Final Answer

120°

Key Points to Remember

Essential concepts to master this topic

Property: Adjacent angles in isosceles trapezoids are supplementary (sum to 180°)
Technique: Set up equation: $(2y+20) + 60 = 180$
Check: Substitute y=50: $2(50)+20 = 120°$ and $120° + 60° = 180°$ ✓

Common Mistakes

Avoid these frequent errors

Using the wrong angle relationship
Don't assume all angles in a trapezoid are equal = wrong setup! Only opposite angles are equal in isosceles trapezoids, but adjacent angles are supplementary. Always remember that adjacent angles (next to each other) must add to 180°.

Practice Quiz

Test your knowledge with interactive questions

True OR False:

In all isosceles trapezoids the base Angles are equal.

FAQ

Everything you need to know about this question

Why do angles B and D add up to 180° if they're not next to each other?

Great observation! In an isosceles trapezoid, angles B and D are actually adjacent to the same parallel side. Think of them as "co-interior" angles, which always sum to 180°.

How do I know which angles are equal in an isosceles trapezoid?

In an isosceles trapezoid, base angles are equal. So angle A = angle B, and angle C = angle D. The diagram shows this isn't the case here, so we use the supplementary property instead.

What if I get a negative value for y?

Check your algebra! In this problem, $2y = 100$ , so y should be positive. Negative angles don't make sense in geometry, so review your equation setup.

Can I solve this without setting up an equation?

Not easily! Since angle B contains the variable y, you need algebra to find its value. The equation method is the most reliable way to solve angle problems with variables.

How do I remember which angles are supplementary in a trapezoid?

Think of it this way: angles on the same side of the trapezoid (like B and D in this problem) always add to 180°. This is true for any trapezoid, not just isosceles ones!

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