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

Question

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

00:00 Calculate the angles

00:02 Opposite sides are parallel in a parallelogram

00:10 Alternate angles are equal between parallel lines

00:18 The sum of angles on a line equals 180

00:22 Therefore subtract alpha from 180 to find B

00:35 Opposite sides are parallel in a parallelogram

00:40 Alternate angles are equal between parallel lines

00:43 Vertical angles are equal

00:50 And this is the solution to the question

$a$ 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:

$\gamma=20$

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