Secants, Tangents and

Angle Measures

Section 10.6

KNOW

THIS

PROOF

Use Intersecting Chords or Secants

A. Find x.

Answer:

Theorem 10.12

Substitution

Simplify.

Use Intersecting Chords or Secants

A. Find x.

Answer: x = 82

Theorem 10.12

Substitution

Simplify.

Use Intersecting Chords or Secants

B. Find x.

Theorem 10.12

Substitution

Simplify.

Step 1 Find mVZW.

Use Intersecting Chords or Secants

Step 2 Find mWZX.

mWZX = 180 – mVZW Definition of supplementary angles

x = 180 – 79 Substitution

x = 101 Simplify.

Answer:

Use Intersecting Chords or Secants

Step 2 Find mWZX.

mWZX = 180 – mVZW Definition of supplementary angles

x = 180 – 79 Substitution

x = 101 Simplify.

Answer: x = 101

C. Find x.

Theorem 10.12

Substitution

Multiply each side by 2.

Use Intersecting Chords or Secants

Subtract 25 from each side.

Answer:

C. Find x.

Theorem 10.12

Substitution

Multiply each side by 2.

Use Intersecting Chords or Secants

Subtract 25 from each side.

Answer: x = 95

A. 92

B. 95

C. 98

D. 104

A. Find x.

A. 92

B. 95

C. 98

D. 104

A. Find x.

A. 92

B. 95

C. 97

D. 102

B. Find x.

A. 92

B. 95

C. 97

D. 102

B. Find x.

A. 96

B. 99

C. 101

D. 104

C. Find x.

A. 96

B. 99

C. 101

D. 104

C. Find x.

Use Intersecting Secants and Tangents

A. Find mQPS.

Theorem 10.13

Substitute and simplify.

Answer:

Use Intersecting Secants and Tangents

A. Find mQPS.

Theorem 10.13

Substitute and simplify.

Answer: mQPS = 125

B.

Theorem 10.13

Use Intersecting Secants and Tangents

Substitution

Multiply each side by 2.

Answer:

B.

Theorem 10.13

Use Intersecting Secants and Tangents

Substitution

Multiply each side by 2.

Answer:

A. 98

B. 108

C. 112.5

D. 118.5

A. Find mFGI.

A. 98

B. 108

C. 112.5

D. 118.5

A. Find mFGI.

A. 99

B. 148.5

C. 162

D. 198

B.

A. 99

B. 148.5

C. 162

D. 198

B.

Use Tangents and Secants that Intersect Outside a Circle

A.

Theorem 10.14

Substitution

Multiply each side by 2.

Use Tangents and Secants that Intersect Outside a Circle

Subtract 141 from each side.

Multiply each side by –1.

Use Tangents and Secants that Intersect Outside a Circle

Subtract 141 from each side.

Multiply each side by –1.

Use Tangents and Secants that Intersect Outside a Circle

B.

Theorem 10.14

Substitution

Multiply each side by 2.

Use Tangents and Secants that Intersect Outside a Circle

Add 140 to each side.

Use Tangents and Secants that Intersect Outside a Circle

Add 140 to each side.

A. 23

B. 26

C. 29

D. 32

A.

A. 23

B. 26

C. 29

D. 32

A.

A. 194

B. 202

C. 210

D. 230

B.

A. 194

B. 202

C. 210

D. 230

B.

Apply Properties of Intersecting Secants

Theorem 10.14

Substitution

Apply Properties of Intersecting Secants

Multiply each side by 2.

Subtract 96 from each side.

Multiply each side by –1.

Apply Properties of Intersecting Secants

Multiply each side by 2.

Subtract 96 from each side.

Multiply each side by –1.

A. 25

B. 35

C. 40

D. 45

A. 25

B. 35

C. 40

D. 45