Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms Mathematics • 11th Grade

Find ๐‘šโˆ ๐ถ๐ต๐ท.

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Video Transcript

Find the measure of angle ๐ถ๐ต๐ท.

The first thing we can do is identify which angle ๐ถ๐ต๐ท is. Angle ๐ถ๐ต๐ท 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 ๐ด๐ต๐ถ๐ท 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 ๐ด๐ต๐ถ and angle ๐ท๐ถ๐ต must add up to 180 degrees.

We know the measure of angle ๐ท๐ถ๐ต is 59 degrees. And then we can divide up angle ๐ด๐ต๐ถ into two smaller angles, one is angle ๐ด๐ต๐ท, which is 44 degrees, and the other angle is our missing angle, angle ๐ถ๐ต๐ท, 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 ๐ถ๐ต๐ท, 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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