Calculate the Fourth Angle in a Trapezoid: Given Angles 110°, 130°, and 70°

Angle Sum Property with Trapezoid Vertices

ABCD is a trapezoid.

A=110 ∢A=110

B=130 ∢B=130

C=70 ∢C=70

Calculate the size of angle D ∢D .

AAABBBDDDCCC13011070

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find angle D
00:12 The sum of adjacent angles in a trapezoid is always equal to 180
00:26 Substitute appropriate values according to the given data
00:35 Isolate angle D
00:48 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

ABCD is a trapezoid.

A=110 ∢A=110

B=130 ∢B=130

C=70 ∢C=70

Calculate the size of angle D ∢D .

AAABBBDDDCCC13011070

2

Step-by-step solution

The sum of angles in a trapezoid is 360 degrees.

Therefore:

360=A+B+C+D 360=A+B+C+D

Let's substitute the known data into the above formula:

360=110+130+70+D 360=110+130+70+D

360=310+D 360=310+D

We'll move terms and maintain the appropriate sign:

360310=D 360-310=D

50=D 50=D

3

Final Answer

50

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of all interior angles in any quadrilateral equals 360°
  • Technique: Add known angles: 110° + 130° + 70° = 310°
  • Check: Verify sum: 110° + 130° + 70° + 50° = 360° ✓

Common Mistakes

Avoid these frequent errors
  • Using triangle angle sum (180°) instead of quadrilateral sum
    Don't use 180° for trapezoids = getting -130° as answer! A trapezoid has 4 sides, not 3, so it needs the quadrilateral rule. Always use 360° for any four-sided figure including trapezoids.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

Why is the angle sum 360° and not 180°?

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A trapezoid has 4 sides, making it a quadrilateral! Only triangles have angles that sum to 180°. Any 4-sided shape (square, rectangle, parallelogram, trapezoid) always has interior angles totaling 360°.

Does it matter which angle I'm finding?

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Not at all! The method works the same way: subtract the sum of known angles from 360°. Whether you're finding angle A, B, C, or D, the process is identical.

What if my calculated angle seems too big or small?

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Check your arithmetic! In this problem, if you get something like 130° or -50°, you likely made an addition error. Interior angles in quadrilaterals are typically between 10° and 350°.

Can I solve this without knowing it's a trapezoid?

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Yes! The angle sum property works for any quadrilateral - square, rectangle, parallelogram, rhombus, or irregular four-sided figure. They all sum to 360°.

How do I check if my answer is reasonable?

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Add all four angles together: they should equal exactly 360°. Also, each individual angle should be positive and less than 180° for a convex quadrilateral like this trapezoid.

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