# What is the value of a + b? You may assume that the ray is tangent to the circle.

180

128

90

64

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calculistaSee the attached picture to better understand the problem we know that if the ray is tangent to the circle then diameter ABC is perpendicular to ray FC and the value of (a + b) is equal to 90 degrees let's check it step 1 find measure arc DC arc DC=180-54-----> 126 ° ∠DBC=126°------> by central angle step 2 find angle a ° we know that The inscribed angle measures half of the arc it comprises. so ∠a=arc AD/2----> 54/2--->∠a= 27° ∠b=arc DC/2----> 126/2---> ∠b=63° ∠a+∠b=27+63----> 90°------> is ok the answer is a+b is equal to 90 degrees