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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Secants, Tangents, and Angle Measures

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Exercise 27 Page 765

The measure of an angle formed by two lines that intersect outside a circle is half the difference of the measures of the intercepted arcs.

20

Practice makes perfect

Consider the given diagram.

We want to find the value of x. We know that if two lines intersect outside a circle, the measure of the angle formed by the intersection of the lines is half the difference of the measures of the intercepted arcs. 3^(∘) = 1/2((5x-6)^(∘)-(4x+8)^(∘)) Let's solve it for x.

3 = 1/2((5x-6) - (4x+8))

LHS * 2=RHS* 2

6 = (5x-6) - (4x+8)

Distribute - 1

6 = 5x-6 - 4x-8

Add and subtract terms

6 = x-14

LHS+14=RHS+14

20 = x

Rearrange equation

x = 20

Subchapter links

Exercises p.763-767