Opposite angles of isosceles trapezoid
About this video
The video finds angle C in an isosceles trapezoid with a 59 degree base angle. Because base angles are congruent, the other base angle is also 59 degrees, and because the bases are parallel, angle C is supplementary to it: 180 - 59 = 121 degrees.
You'll be able to
- use congruent base angles of an isosceles trapezoid to find a missing angle.
- use parallel lines and supplementary angles to find an angle on the other base.
Key words
- isosceles trapezoid
- A trapezoid whose legs are the same length.
- transversal
- A line that crosses two or more other lines.
- supplementary
- Two angles that add up to 180 degrees.
Transcript
- [Instructor] So we have an isosceles trapezoid here, both of these legs have the same length, and we're asked, what is the measure of angle C up here? Pause this video, have a go at that. Alright, now let's walk through this together. So in another video, we have proven that if you have an isosceles trapezoid, the base angles are going to be congruent.
So if this is 59 degrees, then this is 59 degrees as well. And then from there, we can recognize that DC and AB are parallel, so let me just extend to DC just to make that clear. So let me do it like this. There you go. DC and oops, DC and AB are parallel, and so if this is 59 degrees, and let me actually extend this out a little bit.
And if we make CB transversal, then the corresponding angle up here is also going to be 59 degrees, and that is supplementary with the angle that we're trying to figure out: angle C. Angle C is going to be 180 degrees minus 59 degrees, which is equal to 121 degrees.
And we're done.
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