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

Test your knowledge with interactive questions

Find the measure of the angle \( \alpha \)

949494AAABBBCCC92

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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