Trapezoid Angles. This is the first geometry problem of the year. Hopefully, it won't be the only one. I'm just switching things up a bit. I looked at my list of past problems and noticed that I didn't see the word geometry on it. Then, I just looked on the internet for geometry problems and landed on the one below.
To solve this week's problem in completion, you need to recall the following math skills and information:
✔️ Properties of a trapezoid
✔️ Properties of a triangle
✔️ Properties of parallel lines cut by a transversal
WMP #79 wants us to...
Check back on Saturday, April 2nd for the solution, which will be posted below ⬇️.
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✏️📓 Solution Time! 📓✏️
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Let's jump right in! The shape we're dealing with is a trapezoid. In a trapezoid, the bases are parallel. Even if you didn't know that property of a trapezoid, it is indicated in the image. Notice in the picture there are two bold triangles facing the same direction on the bases; this shows parallelism. This is so useful! Why? Well, the two parallel lines along with the diagonal, allow us to identify alternate interior angles. 😁 Alternate interior angles are congruent! In our case, the alternate interior angles we have allow us to solve for x.
Now that we've found the value of x, we can find the value of y. The x-value can be substituted into an equation while simultaneously solving for the y-value. How? What is it that allows us to do that? The two angles in the trapezoid that contain the variable y, are part of a triangle that also contains the angles that allowed us to solve for x. We can use the property of the sum of the angles of a triangle to solve for y. Recall that the sum of the angles of a triangle is 180°.
...And just like that, we've found the value of the two variables: x = 10, and y = 25.
▪️ Did you remember the geometry properties mentioned above?
▪️ Let me know what you thought about this week's problem in the comments section.
Thank you for solving with me this week. ✏️
Next up WMP! #80. 👍🏿
Cheers!
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