Find Angle B in an Isosceles Trapezoid with 50° Angle

Q: What makes an isosceles trapezoid different from a regular trapezoid?

In an isosceles trapezoid, the two legs (non-parallel sides) are equal in length. This creates special angle relationships: base angles are equal and adjacent angles on each leg sum to 180°.

Q: Why do adjacent angles on the same leg sum to 180°?

This happens because the parallel sides create co-interior angles (same-side interior angles) with each leg. Co-interior angles formed by parallel lines always sum to 180°.

Q: Are opposite angles in an isosceles trapezoid equal?

Only base angles are equal! In this trapezoid: $ ∠A = ∠B $ and $ ∠C = ∠D $. Since D = 50°, then C = 50° too, and since B = 130°, then A = 130°.

Q: What if I'm given a different angle instead?

The same principle applies! If you know any one angle, you can find all others using the two key rules: adjacent angles on same leg sum to 180°, and base angles are equal.

Isosceles Trapezoid Angle Properties

Below is an isosceles trapezoid

If $∢D=50°$

Determine the value of $∢B$ ?

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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 According to the given, it's an isosceles trapezoid

00:09 In a trapezoid, angles on the same leg sum to 180

00:23 Let's substitute the value of D to find B

00:34 Let's isolate angle B

00:46 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is an isosceles trapezoid

If $∢D=50°$

Determine the value of $∢B$ ?

Step-by-step solution

Let's recall that in an isosceles trapezoid, the sum of the two angles on each of the trapezoid's legs equals 180 degrees.

In other words:

$A+C=180$

$B+D=180$

Since angle D is known to us, we can calculate:

$180-50=B$

$130=B$

Final Answer

130°

Key Points to Remember

Essential concepts to master this topic

Rule: Adjacent angles on same leg sum to 180°
Technique: $B + D = 180°$ , so $B = 180° - 50° = 130°$
Check: Verify $130° + 50° = 180°$ and opposite angles are equal ✓

Common Mistakes

Avoid these frequent errors

Using regular trapezoid properties instead of isosceles
Don't assume all angles are different like in a regular trapezoid = wrong angle relationships! In regular trapezoids, angles don't follow the same patterns. Always remember isosceles trapezoids have special properties: base angles are equal and adjacent angles on each leg sum to 180°.

Practice Quiz

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Do isosceles trapezoids have two pairs of parallel sides?

FAQ

Everything you need to know about this question

What makes an isosceles trapezoid different from a regular trapezoid?

In an isosceles trapezoid, the two legs (non-parallel sides) are equal in length. This creates special angle relationships: base angles are equal and adjacent angles on each leg sum to 180°.

How do I know which angles are on the same leg?

Look at the trapezoid's legs (the slanted sides). Angles B and D are both touching the right leg, while angles A and C touch the left leg. Adjacent angles on the same leg always sum to 180°.

Why do adjacent angles on the same leg sum to 180°?

This happens because the parallel sides create co-interior angles (same-side interior angles) with each leg. Co-interior angles formed by parallel lines always sum to 180°.

Are opposite angles in an isosceles trapezoid equal?

Only base angles are equal! In this trapezoid: $∠A = ∠B$ and $∠C = ∠D$ . Since D = 50°, then C = 50° too, and since B = 130°, then A = 130°.

What if I'm given a different angle instead?

The same principle applies! If you know any one angle, you can find all others using the two key rules: adjacent angles on same leg sum to 180°, and base angles are equal.

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