I didn’t know anything before I watched this video.
Some of the things I learned after watching the video were the inscribed angle theorem. The inscribed angle theorem is when an angle goes through a circle the measure of the angle equals have of the arc it intersects. For example, if angle ABC equals thirteen, then arc AC equals twenty six because angle ABC equals half of twenty six. So, you multiply thirteen by two. Another thing that I learned was about the multiple intercepted arcs theorem. That is if two inscribed angles of a circle intercept the same one, then the angles are congruent. So, if angle CAD intersect arc CD and angle CBD also intersects arc CD, then angle A is congruent to angle B. The inscribed right triangle theorem is another theorem I learned about. This theorem is when a right triangle is inscribed in a circle if and only if the hypotenuse of the triangle is a diameter of the circle. So, if right triangle ACB is in circle D, then the hypotenuse AB has to be a diameter of circle D. If it is, then the right triangle is a inscribed right triangle. The last theorem I learned about was the inscribed quadrilateral theorem. The inscribed quadrilateral theorem is when a quadrilateral can be inscribed in a circle if and only if the opposite angles are supplementary. For example if quadrilateral ABCD is in circle E, then angle measure of angle A plus measure of angle C equals 180 and measure of angle B plus measure of angle D equals 180 in order for the quadrilateral to be an inscribed quadrilateral. You can use all of these theorems to find angle measure in the specific triangle that you are given. This is all I learned in the video about Inscribed Angles.
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Questions:
I will answer your first question. In order to find the measures of <'s S and T, we will have to look at the angles directly across from them. For < S we see that < V is a right angle automatically making the measure of < S equal to 90 as well because <'s directly across from each other in a quadrilateral must equal 180 degrees combined. Since we know this applies to all angles we can add < T and U together and equal them to 180, simplify the equation and end up with the answer for x which we would then plug into < T. After simplifying that equation we find that <T= 68.
ReplyDeleteNice blog!! For your second question, we know that the opposite angles need to equal 180. So we can set those two measurements equal to 180. Then, according to the video, we use something called the elimination method, which I've never really heard of before and I'm not entirely sure how to use, but it looks like we multiply the top equation by -2 and the bottom one by 3. We can distribute that and then solve for y, which allows us to solve for x. Hope this helps!!
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