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

Q: Why do angles B and D add up to 180°?

In an isosceles trapezoid, adjacent angles on the same leg are supplementary (add to 180°). This is because the parallel bases create interior angles that must sum to 180°.

Q: Are all four angles equal in an isosceles trapezoid?

No! Only opposite angles are equal. In this case, angles A and C both equal 45°, while angles B and D are 135° and 45° respectively.

Q: What if I got x = 45° as my final answer?

That's only half the solution! Remember that $ ∢B = 3x $, so you need to calculate 3 × 45° = 135° to find angle B.

Q: How do I remember which angles are supplementary?

Think of the same leg rule: angles that touch the same non-parallel side add to 180°. So B + D = 180° and A + C = 180°.

Q: Can I check my answer another way?

Yes! All four angles should add to 360°. With your answers: 135° + 45° + 135° + 45° = 360° ✓

Isosceles Trapezoid Angles with Adjacent Side Properties

In an isosceles trapezoid ABCD

$∢B=3x$

$∢D=x$

Calculate the size of angle $∢B$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In an isosceles trapezoid ABCD

$∢B=3x$

$∢D=x$

Calculate the size of angle $∢B$ .

Step-by-step solution

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!

Final Answer

135°

Key Points to Remember

Essential concepts to master this topic

Rule: Adjacent angles on same leg sum to 180° in isosceles trapezoids
Technique: Set up equation 3x + x = 180°, then solve for x
Check: Verify angles add to 360°: 135° + 45° + 135° + 45° = 360° ✓

Common Mistakes

Avoid these frequent errors

Finding x but not calculating angle B
Don't stop at x = 45° and think that's angle B! This gives the wrong answer since B = 3x, not x. Always substitute back: if x = 45°, then angle B = 3(45°) = 135°.

Practice Quiz

Test your knowledge with interactive questions

Do isosceles trapezoids have two pairs of parallel sides?

FAQ

Everything you need to know about this question

Why do angles B and D add up to 180°?

In an isosceles trapezoid, adjacent angles on the same leg are supplementary (add to 180°). This is because the parallel bases create interior angles that must sum to 180°.

Are all four angles equal in an isosceles trapezoid?

No! Only opposite angles are equal. In this case, angles A and C both equal 45°, while angles B and D are 135° and 45° respectively.

What if I got x = 45° as my final answer?

That's only half the solution! Remember that $∢B = 3x$ , so you need to calculate 3 × 45° = 135° to find angle B.

How do I remember which angles are supplementary?

Think of the same leg rule: angles that touch the same non-parallel side add to 180°. So B + D = 180° and A + C = 180°.

Can I check my answer another way?

Yes! All four angles should add to 360°. With your answers: 135° + 45° + 135° + 45° = 360° ✓

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