Arc XYZ lies on a circle centered at O. Is a

Question

https://gmatclub.com/forum/download/file.php?id=25369 Arc XYZ lies on a circle centered at O. Is a < 55? (1) Angle ZOY = 35 (2) Angle XOY = 75 Kudos for a correct solution . Q14_1.png

chetan2u · Answer

ans C...
 both statements are required to get angle zox which is equal to 2a..

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION: The correct response is (C). If we draw a radius from O to Y, we can fill in the two given values: ZOY = 35, and XOY = 75. OX and OZ are both radii of the same circle, so their opposite angles must be equal. We can use this information to solve for angle XYZ, and in term find the value for a. To do the math, here’s how it would look: Q14_2.png 180 = 35 + OYZ + OZY 145/2 = 72.5 = OYZ = OZY 180 = 75 + OXY + OYX 105/2 = 52.5 = OXY + OYX Angle XYZ = 72.5 + 52.5 = 125 Angle a = 180 – 125 Angle a = 55 The answer to the question would always be “no.” If you chose (A), this would allow us to solve for XYO, but we’d also need angle OYZ to find a. If you chose (B), this would allow us to find OYZ, but we’d also need to know angle XOY to find angle XYO. If you chose (D), both pieces of information are important, but neither is independently sufficient. If you chose (E), you may have missed that XO = OY = OZ, since all radii in a circle must be equal, as well as the fact that angles opposite equal sides are also equal.

joylive · Answer

Bunuel ,

can the solution be like this ?

an inscribed angle is exactly half the corresponding central angle, so all inscribed angle that subtends to the same arc, are equal.
so - 75+35 = 110/2 = 55 ?

Nadiuska · Answer

Hi there,

How do you guys know zox is 2a?

Thanks!

rohit8865 · Answer

here is alternate solution
please follow attached fig.
(1)ZOY=35 means YXZ=17.5 (central angle theorem)
not suff....
(2) similarly XOY=75 means XZY = 37.5
not suff...

combining both as angle a = sum of 2opp.internal angles of the triangle XYZ
so a=37.5+17.5----------->55
suff...

Ans C

rohit8865 · Answer

Ans is C as both internal angles of triangle XYZ is known and is nothing but sum of those angles =a=55

Ans C

rnz · Answer

why are 145 and 105 divided by 2? Is it because they're inscribed angles?

kaleem765 · Answer

Another way to solve this question would be to use the concept of central angle and inscribed angle i.e. inscribed angle is half of the central angle.

bumpbot · Answer

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Arc XYZ lies on a circle centered at O. Is a < 55?

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