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math b regents january 2005 multiple choice #10?

a small fragment of something brittle, such as pottery, is called a shard. In a diagram, ray BC is a tanget to arc AB at B and the measure of angle ABC=45, what is the measure of arc AB , the outside edge of the arc
WHY IS THE ANSWER 90 DEGREES EXPLAIN HOW TO GET THAT AND EXPLAIN EACH STEP

It is easier to draw this out. First draw a line from the center of the circle (X) to B. the angle between BC and XB is 90 degrees (definition of tangent). Thus angle ABX is 45 degrees (90 – angle ABC). Consider triangle ABX, AX = XB = radius i.e., isosceles triangle. Thus angle XAB = angle ABX = 45 degrees (angles opposite equal sides in an isosceles triangle are equal). Thus, Angle AXB = 180 – angle ABX – angle XAB = 180 – 45 – 45 = 90.

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