O is the center. AB||CD. Find y. (a) 24.5° (b) 110° (c) 60° (d) 55°

Mathematics

1 answer:

Leno4ka [110]3 years ago

5 0

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

_____

Comment on units

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.

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