GEOMETRY
MODULE 5 LESSON 15
SECANT ANGLE THEOREM – EXTERIOR CASE
Secant Angle Theorem – Exterior Case: The measure of an angle whose
vertex lies in the exterior of a circle, and each of whose sides intersect the
circle in two points, is equal to half the difference of the angle measures of
its larger and smaller intercepted arcs.
PRACTICE
Together, we will complete exercise 1 and 2 on page 118 of your workbook.
1.
2.
𝑥=
82 − 26
= 28°
2
̂ = 360 − 252 = 108
𝐷𝐸
𝑥=
252 − 108
= 72°
2
ON YOUR OWN
Complete exercise 3 on page 118.
̂ − 𝐸𝐹
̂
𝐵𝐷
2
̂ = 𝐸𝐵
̂
𝐹𝐷
𝑥=
̂ = 145 − 𝐸𝐹
̂
215 − 𝐵𝐷
̂ − 𝐸𝐹
̂
215 − 145 = 𝐵𝐷
̂ + 𝐹𝐷
̂ = 215
𝐵𝐷
̂ − 𝐸𝐹
̂ = 70
𝐵𝐷
̂ + 𝐸𝐵
̂ = 360 − 215 = 145
𝐸𝐹
̂ + 𝐹𝐷
̂ = 145
𝐸𝐹
𝑥=
̂ = 215 − 𝐵𝐷
̂
𝐹𝐷
̂ − 𝐸𝐹
̂
𝐵𝐷
70
=
2
2
𝑥 = 35°
̂ = 145 − 𝐸𝐹
̂
𝐹𝐷
1
MOD5 L15
HOMEWORK
Problem Set Module 5 Lesson 15, page 121.
#2, #3, #4 and #5. You must show all calculations and/or state an explanation!
DUE: Tuesday, May 9, 2017
THE INSCRIBED ANGLE THEOREM AND ITS FAMILY OF THEOEMS
2
MOD5 L15