Answer: Third choice, 160 degrees
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Step-by-step explanation:
See the attached image below to see one way you could draw the diagram based on the given info. The drawing is not to scale.
The color coded angles hopefully let you see which angles are congruent to one another
- Angle EXB = Angle DXE (in red)
- Angle CXD = Angle DXB (in blue)
- Angle AXC = Angle CXB (in green)
These three pairs of congruences are possible because of the angle bisections that occur.
Since EXB is 20, this means DXE is 20 as well. They combine to 20+20 = 40, which is the measure of angle DXB (angle addition postulate).
Angle DXB is congruent to CXD, so both are 40 and they combine to 40+40 = 80. This is the measure of angle CXB.
Finally, angle CXB = 80 doubles to 160 which is the measure of angle AXB. Or you could say
angle AXB = (angle AXC) + (angle CXB) = 80 + 80 = 160.