Find Angle A in a Rhombus with 50° Interior Angle Measurement

Q: How do I know which angles are opposite in a rhombus?

Opposite angles are the ones that don't share a side. In this rhombus, angle A is at the top vertex, so it's opposite to the angle at the bottom vertex. They're separated by the maximum distance.

Q: Are all angles in a rhombus equal?

Not necessarily! Only opposite angles are equal. Adjacent angles (next to each other) are supplementary, meaning they add up to 180°. So if one angle is 50°, the adjacent angle is 130°.

Q: What's the difference between a rhombus and a square?

A square is a special rhombus where all angles are 90°. A regular rhombus can have different angle measures, but opposite angles are always equal and adjacent angles always add to 180°.

Q: Why is the rhombus drawn this way?

The rhombus is positioned like a diamond to help you visualize the angle relationships clearly. The 50° marking shows you one angle, and you need to find its opposite partner.

Rhombus Properties with Opposite Angles

Determine angle $∢A$ in the given rhombus:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find angle A

00:03 Angle D according to the given data

00:08 In a rhombus opposite angles are equal

00:14 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

Determine angle $∢A$ in the given rhombus:

Step-by-step solution

The rhombus is a type of parallelogram, therefore its opposite angles are equal (property of parallelograms), so:

$∢A =50\degree$ Hence, the correct answer is answer A.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite angles in a rhombus are always equal
Technique: Identify opposite vertices: A is opposite to the 50° angle
Check: Verify that angles A and C both equal 50° ✓

Common Mistakes

Avoid these frequent errors

Adding angles instead of identifying opposite pairs
Don't add 50° + other angles to find A = wrong calculation! This confuses angle relationships and gives incorrect results. Always identify which angles are directly opposite each other in the rhombus.

Practice Quiz

Test your knowledge with interactive questions

Look at the following rhombus:

Are the diagonals of the rhombus parallel?

FAQ

Everything you need to know about this question

How do I know which angles are opposite in a rhombus?

Opposite angles are the ones that don't share a side. In this rhombus, angle A is at the top vertex, so it's opposite to the angle at the bottom vertex. They're separated by the maximum distance.

Are all angles in a rhombus equal?

Not necessarily! Only opposite angles are equal. Adjacent angles (next to each other) are supplementary, meaning they add up to 180°. So if one angle is 50°, the adjacent angle is 130°.

What's the difference between a rhombus and a square?

A square is a special rhombus where all angles are 90°. A regular rhombus can have different angle measures, but opposite angles are always equal and adjacent angles always add to 180°.

How can I double-check my answer?

Remember that all four angles in any quadrilateral must add up to 360°. If opposite angles are both 50°, then: 50° + 130° + 50° + 130° = 360° ✓

Why is the rhombus drawn this way?

The rhombus is positioned like a diamond to help you visualize the angle relationships clearly. The 50° marking shows you one angle, and you need to find its opposite partner.

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