Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms | Nagwa Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms | Nagwa

Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms Mathematics

Find πβ πΆπ΅π·.

01:28

Video Transcript

Find the measure of angle πΆπ΅π·.

The first thing we can do is identify which angle πΆπ΅π· is. Angle πΆπ΅π· is here. From there, we need to think about what we can say about this shape. Since this quadrilateral has two pairs of parallel sides, we can say that π΄π΅πΆπ· is a parallelogram. And based on the properties of parallelograms, we know that in a parallelogram adjacent angles sum to 180 degrees, which means that angle π΄π΅πΆ and angle π·πΆπ΅ must add up to 180 degrees.

We know the measure of angle π·πΆπ΅ is 59 degrees. And then we can divide up angle π΄π΅πΆ into two smaller angles, one is angle π΄π΅π·, which is 44 degrees, and the other angle is our missing angle, angle πΆπ΅π·, which means we can solve this equation for our missing angle. 44 plus 59 is 103 degrees. And that means to find the measure of angle πΆπ΅π·, we can subtract 103 degrees from both sides of the equation. And we see that our missing angle must measure 77 degrees.

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