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21 May 2017, 17:07
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MisterEko
Here the quickest method is to recognize that the arcs are in proportion to each other. The ratio is 1:2:6:9, with 1 as the smallest arc, BZC, 2 as the second largest arc, AXB, and thus by definition 6 as the largest arc. The angles corresponding to these arcs will be in the same proportion, so 9x = 180 and x = 20, the hidden multiplier. The angle C on the triangle corresponds to the 2 value in the ratio, so the product is 2(20) = 40.
04 Sep 2017, 20:19
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Can someone explain something to me here?
When I first looked at this, I noted the proportions: x, 2x, 6x. When you sum it up, you get 9x. However, I set 9x=360. I understand some posts are setting this equation equal to 180 because angles in a triangle sum up to 180 and the question is asking for the measure of an angle in a triangle...but since the triangle is inscribed in the circle, i was confused and set it equal to 360 b/c thats the sum of angles in a circle.
allow me to expand: when i set 9x=360, i get x=40. since angle BCA represents arc AXB, i know the value here is 2x. 2(40) = 80 degrees. HOWEVER, inscribed angles are HALF of the central angle. so what i did was halve 80 to get 40. so...same (correct) answer, different way.
can anyone explain if my way is correct/incorrect? and shed some light into the question i asked above? thank you!
When I first looked at this, I noted the proportions: x, 2x, 6x. When you sum it up, you get 9x. However, I set 9x=360. I understand some posts are setting this equation equal to 180 because angles in a triangle sum up to 180 and the question is asking for the measure of an angle in a triangle...but since the triangle is inscribed in the circle, i was confused and set it equal to 360 b/c thats the sum of angles in a circle.
allow me to expand: when i set 9x=360, i get x=40. since angle BCA represents arc AXB, i know the value here is 2x. 2(40) = 80 degrees. HOWEVER, inscribed angles are HALF of the central angle. so what i did was halve 80 to get 40. so...same (correct) answer, different way.
can anyone explain if my way is correct/incorrect? and shed some light into the question i asked above? thank you!
04 Sep 2017, 22:41
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LakerFan24
Sum of the angles of a triangle is ALWAYS 180.
So, angle BAC, angle ABC and angle BCA add up to 180 degrees.
The angles around the centre of a circle will add up to a complete 360 degrees. So in this fig: https://gmatclub.com/forum/the-length-o ... l#p1235120
Angles AOB, BOC and COA add up to 360 degrees.
If you assume that x is angle subtended at the centre by arc BZC, you do get x + 2x + 6x = 360 and subsequently the correct answer.
