SOLUTION: In circle O, AX and BY intersect at E. If Angle BXY = 40°, Angle YBX = 55°, and intercepted arc BA = 70°. Find the measure of arc AB, arc BX, arc YZ, arc AY, arc ABX

Algebra ->  Circles -> SOLUTION: In circle O, AX and BY intersect at E. If Angle BXY = 40°, Angle YBX = 55°, and intercepted arc BA = 70°. Find the measure of arc AB, arc BX, arc YZ, arc AY, arc ABX       Log On


   

Question 1173327: In circle O, AX and BY intersect at E. If Angle BXY = 40°, Angle YBX = 55°, and intercepted arc BA = 70°. Find the measure of arc AB, arc BX, arc YZ, arc AY, arc ABX
Answer by greenestamps(13200) About Me  (Show Source):
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(1) The sum of the measures of all the arcs of the circle is 360.

(2) The measure of any arc is twice the measure of the inscribed angle that cuts off that arc.

(3) The sum of the measures of the angles of a triangle is 180. (Note that this follows from (1) and (2), using triangle BXY....)

Given:
(a) angle BXY = 40
(b) angle YBX = 55
(c) arc BA = 70

To find:

arc AB: given

arc BX: cut off by angle BYX, whose measure can be determined from (3)

arc YZ (I will assume that is supposed to be YX): cut off by given angle YBX; use (2)

arc AY: Use (1); you know the measures of all the other arcs

arc ABX: sum of the measures of arcs AB and BX