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

Question

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

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!

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

As they are adjacent and theredore complementary angles to 180:

$180-30=150$

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

$\gamma=20$

$\alpha=30$ $\beta=150$ $\gamma=20$