Grades 7-8 Video Solutions 2023-2023_7-8

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Question 16. Triangle ABC is isosceles, with angle ABC equal to 40 degrees. The two marked angles, angle EAB and angle DCA are equal. What is the size of angle CFE?  Let's start off by taking a closer look at our triangle, marking out our points and various lines drawn. We know that angle ABC is equal to 40 degrees.  Next, we know that angles EAB and DCA are equal to each other, so we can write that out. Likewise, since this is an isosceles triangle, we can write out that angle CAE is equal to  angle BCD. To simplify this, let's call these angles X and Y for now. Since we know that a triangle always has three angles equal to 180, we can set up a formula like so.  X plus Y plus X plus Y plus 40 equals 180. If we simplify this, we get 2X plus 2Y equal to 140, and then once we divide the two out, we get X plus Y equal to 70.  With this, we can make a new formula, X plus Y plus angle AFC equal to 180. Since we know that triangle AFC is also a triangle, its angles will total 180.  Knowing that X plus Y equals 70, we can subtract from both sides and get angle AFC equal to 100 in time. Now that we know this angle, we can try to find out the angle CFE.  With this, we simply have to do 2 times angle AFC plus 2 times angle CFE equal to 360, since a circle will always equal 360.  Using this, we simplify, and we get angle AFC plus angle CFE equal to 180, and since we already know angle AFC is equal to 110, we have 110 plus angle CFE equal to 180.  With this, we subtract 110 from both sides and get our answer, angle CFE is equal to 70 degrees D.

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