SOLUTION: In a circle O, AX and BY intersect at E. If angle BXY = 40°, angle YBX = 55°, and arc BA = 70°, find the measure of angle BAX, angle XEY, angle XAY, angle AXB, angle AXY, and an
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-> SOLUTION: In a circle O, AX and BY intersect at E. If angle BXY = 40°, angle YBX = 55°, and arc BA = 70°, find the measure of angle BAX, angle XEY, angle XAY, angle AXB, angle AXY, and an
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Question 1173345: In a circle O, AX and BY intersect at E. If angle BXY = 40°, angle YBX = 55°, and arc BA = 70°, find the measure of angle BAX, angle XEY, angle XAY, angle AXB, angle AXY, and angle YBX Answer by greenestamps(13198) (Show Source):
(1) The sum of the measures of the arcs of a circle is 360 degrees.
(2) The sum of the measures of the angles of a triangle is 180 degrees.
(3) The measure of an angle inscribed in a circle is half the measure of the intercepted arc.
(4) The measure of an angle formed by two chords of a circle is the average of the measures of the two arcs intercepted by the chords.
The measures of angles YBX and BXY are given; use (2) to find the measure of angle BYX.
Use (3) and the given measure of arc AB to find the measures of all the arcs of the circle.
Then....
angle BAX: (3) with arc BX
angle XEY: (4), with arcs AB and XY
angle XAY: (3), with arc XY
angle AXB: (3), with (given) arc AB
angle AXY: (3), with arc AY
angle YBX: (given)
