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### Course: High school geometry (staging)>Unit 9

Lesson 8: Inscribed shapes problem solving

Example showing supplementary opposite angles in inscribed quadrilateral.

## Want to join the conversation?

• I don't quite get how khan got 90 degrees for the small arc.
• We know that the measure of an arc is DOUBLE the measure of the Inscribed Angle. In this case, the angle WIL is inscribed by the blue arc. The measure given for this angle is 45 degrees.
So, the measure of the blue arc is 45*2=90 degrees.

I hope you got that now.
• Okay, this is basically turning my mind to mush. How are the angles always supplementary? Where did he get 90 degrees from? I'm confused, please help me.
• Angles for inscribed quadrilaterals are always supplementary. It's one of those weird facts of math that they don't normally explain, like why you divide before adding, etc. If you do some research, you can likely find some proof for why inscribed quadrilaterals are always supplementary, but it's not something normally covered in math courses. Sal got the 90 degrees by multiplying 45 by 2. This is because of one of the theorems that states that inscribed angles are 1/2 of the degree measure of the arc they intercept. Hope this helped.
(1 vote)
• You can just do 180-45 because the opposite angles of a quadrilateral have a sum of 180 degrees.
• I still not understanding the math its really stressing to learn about the subject but am getting there
• is the opposite of angle WDL a valid inscribed angle
• WIL, ILD, LDW and DWI are all inscribed angles

An inscribed angle is the angle formed from the intersection of two chords, and a chord is a line segment that has each end point on the side of the circle somewhere.

So there are 4 chords, WI, IL, LD and DW and each place they intersect forms an inscribed angle.

I assume by opposite you mean WIL, but all angles there are inscribed angles.

Let me know if this did not help.
• at in video he talks about the sums being supplementary. are they Always supplementary? how can you tell if they are or not?
• From what Sal said in the video after that point, he implies that they are always that way and he is going to prove it in a later video.
• Wait, the angle is not inscribed? What?
• At what point exactly in the video you're getting confused? Let us know so we can help!
(1 vote)
• I thought triangles could only add up to 180 not 289
• It is not triangle there it's an quadrilateral