I figured this out without trigonometry, but the video shows both a trig and a non-trig method.
My answer will be in the comments.
Tuesday, May 16, 2023
1 comment:
READ THIS BEFORE COMMENTING!
All comments are subject to approval before they are published, so they will not appear immediately. Comments should be civil, relevant, and substantive. Anonymous comments are not allowed and will be unceremoniously deleted. For more on my comments policy, please see this entry on my other blog.
AND A NEW RULE (per this post): comments critical of Trump's lying must include criticism of Biden's or Kamala's or some prominent leftie's lying on a one-for-one basis! Failure to be balanced means your comment will not be published.
Subscribe to:
Post Comments (Atom)
My non-trig method:
ReplyDeleteDraw a line segment connecting the vertex of the supplemental angle to y with the vertex of the supplemental angle to x. You've just divided the blue region into two triangles: one isosceles (I'll justify this in a second), and one right.
The white triangle on the left has a hypotenuse of 13 (Pythagorean triple: 5:12:13). The segment connecting x and y also has a length of 13 for the same reason, so the bigger of the two blue-region triangles is a 45-45-90 right triangle (along with being isosceles).
The smaller blue-region right triangle (upper-right corner) has the same side lengths and angle measures as the left-hand white right triangle. This means the larger acute angle inside the smaller blue right triangle also measures y degrees.
So angle x remains mysterious, but we don't have to solve for x—only for x + y. We know that x + y + 45 (from the 45-45-90 triangle) = 180, so x + y = 135º.
QED. I did this on paper, then belatedly realized I could have done most or all of this in my head.
The trig method shown in the video is a bit above my pay grade.