Answer:
(d) 55°
Step-by-step explanation:
Because segment AB is parallel to CD, ∠OAB will also have measure y°. (It is an alternate internal angle with ∠COA created by transversal AO.)
We assume that arc AB, marked "70", has a measure of 70°, which means ∠AOB = 70°.
ABO is an isosceles triangle, so its base angles are equal and the sum of its internal angles is 180°.
... y° + y° + 70° = 180°
... 2y = 110
... y = 55
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<em>Comment on units</em>
The number 70 is not marked as degrees, so we could take it as either an angle measure or an actual length (in which case the problem cannot be worked). A unitless angle measure is radians, but 70 radians makes no sense in this context. (70 radians is 11 full circles plus about 50.7°. "y" would have to be a rather large negative number for the angle measures to sum to 180° in triangle AOB.)
The value of y we found above is 55, so y° is then 55°. It makes no sense in this context for y to be called 55°, because the angle measure would then be ...
... 55°°
a value that has no meaning as an angle measure.
