Question Video: Finding the Measure of an Angle in a Parallelogram Using the Properties of Parallelograms | Nagwa Question Video: Finding the Measure of an Angle in a Parallelogram Using the Properties of Parallelograms | Nagwa

# Question Video: Finding the Measure of an Angle in a Parallelogram Using the Properties of Parallelograms Mathematics

In the figure below, given that π΄π΅πΆπ· is a parallelogram, find πβ π΄.

02:06

### Video Transcript

In the figure below, given that π΄π΅πΆπ· is a parallelogram, find the measure of angle π΄.

In this question, weβre given that there is a parallelogram, and we need to find one of the angles in this parallelogram. So, letβs recall what we know about the angles. We can remember that in a parallelogram, opposite angles are equal. Weβre asked to find the measure of angle π΄. And if we know the angle at πΆ, then these would be equal. If we look at the diagram, this angle πΆπ·πΉ, we donβt know the value of. And if we wanted to work out the angle π΄ directly, weβd need to know this angle at π΄π·πΈ. But we donβt.

There is another option to work out the measure of angle π΄. And that is, if we know the angle at π· or the angle at π΅. Letβs see if we can calculate this angle at π΅. Letβs highlight this quadrilateral within the shape π·πΈπ΅πΉ. We have a right angle here at angle π·πΈπ΄. As it lies on the straight line π΄π΅, then we can also say that there is a 90 degree or right angle here at π·πΈπ΅. So, in this quadrilateral π·πΈπ΅πΉ, we have three angles that we know and one that we donβt know. We can use the fact that the angles in any quadrilateral sum to 360 degrees to find the measure of angle π΅.

So, angle π΅ is 130 degrees. Because opposite angles in a parallelogram are equal, then π΅ and π· are both 130 degrees. So, letβs go back to looking at π΄π΅πΆπ·. As the sum of the angles in this parallelogram will be 360 degrees, if we take away two lots of 130 degrees from 360 degrees, then we know that π΄ and πΆ will add to 100 degrees.

Since we know that π΄ and πΆ are equal, then both of these would be 50 degrees. So, the measure of angle π΄ is 50 degrees.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions