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

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

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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:

180−30=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

Practice Quiz

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If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

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