Rhombus Angle Calculation: Finding Angle A When B = 80 Degrees

Rhombus Properties with Consecutive Angle Calculation

ABCD rhombus.

B=80 ∢B=80

Calculate the size A ∢A

AAABBBDDDCCC80

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 First, let's find angle A.
00:14 In a rhombus, opposite angles are always equal.
00:32 Remember, the sum of angles in any quadrilateral is 360 degrees.
00:44 Now, let's substitute the right values to find angle A.
01:03 Next, we'll gather like terms and isolate angle A.
01:29 And that's how we solve for angle A in this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

ABCD rhombus.

B=80 ∢B=80

Calculate the size A ∢A

AAABBBDDDCCC80

2

Step-by-step solution

According to the properties of a quadrilateral, each pair of opposite angles are equal to each other.

Therefore:

B=C=80 B=C=80

A=D A=D

Additionally, we know that the sum of the angles in a quadrilateral equals 360 degrees.

Therefore, we can calculate angles A and D as follows:

3608080=200 360-80-80=200

200:2=100 200:2=100

Angle A is equal to 100.

3

Final Answer

100

Key Points to Remember

Essential concepts to master this topic
  • Property: In a rhombus, consecutive angles are supplementary (add to 180°)
  • Technique: If angle B = 80°, then angle A = 180° - 80° = 100°
  • Check: Verify all angles sum to 360°: 100° + 80° + 100° + 80° = 360° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all angles in a rhombus are equal
    Don't think all angles equal 90° like in a square = wrong 90° answer! A rhombus can have any angles as long as opposite angles are equal and consecutive angles are supplementary. Always use the supplementary angle rule: consecutive angles add to 180°.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

Isn't a rhombus the same as a square?

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Not always! A square is a special type of rhombus where all angles are 90°. But most rhombuses have different angle measures - they just need opposite angles equal and consecutive angles supplementary.

Why are consecutive angles supplementary in a rhombus?

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Because a rhombus is a parallelogram! In any parallelogram, consecutive angles are supplementary (add to 180°). This is a fundamental property you can always rely on.

How do I remember which angles are opposite?

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Think of it like corners of a rectangle! Angle A is opposite to angle C, and angle B is opposite to angle D. They're diagonally across from each other.

What if I'm given a different angle instead of angle B?

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The method stays the same! If you know any angle in a rhombus, you can find all others using:

  • Consecutive angles: 180° - given angle
  • Opposite angle: Same as given angle

Can I solve this problem a different way?

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Yes! You could use the fact that all four angles sum to 360°. Since opposite angles are equal: 2A + 2B = 360°, so 2A + 2(80°) = 360°, giving A = 100°.

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