Calculate Parallelogram Angles: Finding α and β with Given 30° and 20°

Parallelogram Angles with Alternate Interior Lines

Look at the parallelogram in the diagram. Calculate the angles indicated.

3020βα

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's calculate the angles.
00:08 Remember, in a parallelogram, opposite sides are parallel.
00:16 This means alternate angles are equal when lines are parallel.
00:24 The sum of angles on a straight line is 180 degrees.
00:29 So, subtract angle Alpha from 180 to find angle B.
00:41 Again, opposite sides in a parallelogram are parallel.
00:46 Thus, alternate angles are equal between these lines.
00:51 Also, vertical angles are always equal.
00:56 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the parallelogram in the diagram. Calculate the angles indicated.

3020βα

2

Step-by-step solution

a a is an alternate angle to the angle that equals 30 degrees. That meansα=30 \alpha=30 Now we can calculate: β \beta

As they are adjacent and theredore complementary angles to 180:

18030=150 180-30=150

Angleγ \gamma Is on one side with an angle of 20, which means:

γ=20 \gamma=20

3

Final Answer

α=30 \alpha=30 β=150 \beta=150 γ=20 \gamma=20

Key Points to Remember

Essential concepts to master this topic
  • Property: Opposite angles in parallelograms are equal and congruent
  • Technique: Use alternate angles: α = 30° since they're on parallel lines
  • Check: Adjacent angles sum to 180°: 30° + 150° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Confusing alternate and corresponding angles
    Don't assume α equals the 20° angle just because they look similar = wrong identification! The 20° and α are not alternate angles. Always trace the parallel lines carefully and identify which angles are actually alternate to each other.

Practice Quiz

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Does the drawing show an adjacent angle?

FAQ

Everything you need to know about this question

How do I know which angles are alternate?

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Alternate angles are on opposite sides of the transversal line and between parallel lines. They form a 'Z' pattern when you connect them visually.

Why is β = 150° and not 30°?

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α and β are adjacent angles in the parallelogram, so they must add up to 180°. Since α = 30°, then β = 180° - 30° = 150°.

What's the difference between alternate and corresponding angles?

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Alternate angles are on opposite sides of the transversal and equal each other. Corresponding angles are in the same relative position and also equal, but they're on the same side of the transversal.

Do I need to know all angle properties for parallelograms?

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Yes! Remember:

  • Opposite angles are equal
  • Adjacent angles sum to 180°
  • All angles sum to 360°
These properties work together to solve angle problems.

How can I check my parallelogram angle answers?

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Use the angle sum property: all four angles should add to 360°. Also verify that opposite angles are equal and adjacent angles sum to 180°.

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