Find Angle B in Quadrilateral ABCD: Using 140° and 80° Measurements

Quadrilateral Angle Sum with Three Known Angles

ABCD is a quadrilateral.

According to the data, calculate the size of B ∢B .

AAABBBDDDCCC80140

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find angle B
00:09 The sum of angles in a quadrilateral is always equal to 360
00:15 Substitute appropriate values according to the given data
00:35 Collect terms and isolate D
00:55 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 quadrilateral.

According to the data, calculate the size of B ∢B .

AAABBBDDDCCC80140

2

Step-by-step solution

As we know, the sum of the angles in a square is equal to 360 degrees, therefore:

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

We replace the data we have in the previous formula:

360=140+B+80+90 360=140+B+80+90

360=310+B 360=310+B

Rearrange the sides and use the appropriate sign:

360310=B 360-310=B

50=B 50=B

3

Final Answer

50

Key Points to Remember

Essential concepts to master this topic
  • Rule: All quadrilateral interior angles sum to exactly 360°
  • Technique: Add known angles: 140° + 80° + 90° = 310°
  • Check: Verify sum: 140° + 50° + 80° + 90° = 360° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming quadrilateral angles sum to 180°
    Don't use 180° as the angle sum for quadrilaterals = wrong answer every time! This is the triangle angle sum rule. Always remember quadrilaterals have four angles that sum to 360°.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

Why do quadrilateral angles add up to 360° instead of 180°?

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A quadrilateral can be divided into two triangles by drawing a diagonal. Since each triangle has angles summing to 180°, the quadrilateral total is 2 × 180° = 360°.

Does this rule work for all quadrilaterals?

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Yes! Whether it's a square, rectangle, rhombus, trapezoid, or irregular quadrilateral, the interior angles always sum to 360°. The shape doesn't matter!

What if I can't see all the angle measurements clearly?

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Look for right angle symbols (small squares) which indicate 90°. Also check if any sides are marked as parallel, which can help you identify equal angles.

How do I know which angle is angle B in the diagram?

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Follow the vertices in alphabetical order: A → B → C → D. The angle at vertex B is the interior angle formed by sides AB and BC meeting at point B.

Can I solve this if one of the given angles was actually an exterior angle?

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Be careful! This method only works with interior angles. If you have an exterior angle, first convert it: interior angle = 180° - exterior angle.

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