Question Video: Using the Properties of Parallelograms to Solve a Problem Mathematics • 11th Grade

In the following figure 𝐴𝐵𝐶𝐷 is a parallelogram. What is the measure of ∠𝐴?


Video Transcript

In the following figure, 𝐴𝐵𝐶𝐷 is a parallelogram. What is the measure of angle 𝐴?

In this question, we can see that there’s a parallelogram drawn in red, 𝐴𝐵𝐶𝐷. And we also have a protractor here which helps us measure the size of the angle. You might think that it’s not very helpful here as we’re asked for the measure of angle 𝐴 and the protractor isn’t at angle 𝐴. However, we can use the fact that in a parallelogram, the opposite angles are equal. So, that means that angle 𝐴 and angle 𝐶 will be equal in size. So let’s go ahead and find the measure of angle 𝐶.

This protractor is nicely set in place. We have one of the long sides on our protractor set along one of the edges of the angle. We have the center of the protractor lied correctly on the vertex. We need to read off the correct value in order to find the measure of the angle. One of the most common problems when we’re using a protractor is working out which of the values we want to use. Is it this value at the top which we can see is exactly between 100 and 110 which means it’s 105 degrees? Or do we use the values here closer to the center? In this case, it’s between 70 and 80, which is 75 degrees. So which one do we use?

Remember that we’re trying to find this angle at 𝐶 internally in the parallelogram. So, we want to start where the protractor is at zero, that’s the external numbers, and read all the way around the outside, which means that we’re using the value of 105 degrees. The angle here that measures 75 degrees would be the exterior angle. We would start from zero and read all the way around until we get to 75 degrees. But as we need the interior angle at 𝐶, then we use 105 degrees. Remember that we’re asked for the angle of 𝐴 and using the fact that the opposite angles are equal, then we can give our answer of 105 degrees.

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