At first, I was having difficulty understanding the given. I thought the PQ, PR and QR are the lengths of the triangle, but they are actually the arc (angle measure).
Anyway, to get x, we know that the measure of a circle is 360 degrees. We get the sum of arcs PQ, PR and QR and equate it to 360:
(8x - 10) + 6x + (10x + 10) = 360
24x = 360
x = 15
now we substitute this back to the measure of the arcs:
PQ = 8*15 - 10 = 110 degrees
PR = 6*15 = 90 degrees
QR = 10*15 + 10 = 160 degrees
Then, recall inscribed angle theorem. The measure of an inscribed angle (in this case, an interior angle of the triangle) is half the measure of the arc it subtends. Thus the interior angles of the triangles are half of PQ, PR and QR, which are 55, 45 and 80.
The triangle is SCALENE because there are no angles of equal measure.
hope this helps~ :)
a. To find X, you will need to add the arc measures together and set this expression equal to the total degrees of a circle and then solve for X. Must show all work.
b. Here are the steps to take (show all work)
1. Plug your x-value from a into each of the arc measures to find what each ars measures.
2. Apply the Inscribed Angles Theorem to then find <P, <R, and <S
3 Use the angle measure from step 2 above to determine what type of triangle yoy have.
the picture is a circle with triangle inscribed top point being P the bottom left being Q and bottom right being R. The left side (8x-10), right side (6x), and bottom (10x+10).
I have been given the answer but I need to know how to get to that.Can someone PLEASE help!!
Answer:
a. x=15
b. scalene the arc measures are 110, 90, 160, the arcs are not congruent neither are the chords that intercept.
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Thank you didn't think I was ever gonna get help with this one. You explained it so well that it makes sense now.Thank you again
1 answer