Exercise 19 Page 815

Consider the given diagram.

We will find the values of a and b one at a time.

Finding a

The measure of an angle formed by two lines that intersect inside a circle is half the sum of the measures of the intercepted arcs. The angle formed by the intersection of the lines inside the circle measures a^(∘), and the measures of the intercepted arcs are 45^(∘) and 145^(∘).

With this information, we can write an equation and solve it to find the value of a.

a=1/2(145+45)

AddTerms

Add terms

a=1/2(190)

MoveRightFacToNumOne

1/b* a = a/b

a=190/2

CalcQuot

Calculate quotient

a=95

Thus, the value of a is 95.

Finding b

A chord is a straight line that goes from a point to another point on the circle.

Therefore, by the Angle Addition Postulate, we have that 95 and b add up to 180.

95+ b=180 ⇔ b= 85

Thus, the value of b is 85.