1. Module 1- Lesson 7 and 8
Finding Unknown Angle Measures – Transversals and Auxiliary Lines
Finding Unknown Angle Measures in Triangles

2. DO NOW ∡ ∡ ∡ ∡ Module 1 – lesson 7 p. S41 X+8 +2x -8 = 90 3x = 90
Angle Addition Postulate
3x = 90
X = 30
Y = 2x-8
30 𝑜
Verticals Angles Theorem
Y = 2(30)-8
52 𝑜
Substitution
Y = 60-8
Y = 52
∡𝐴𝑂𝐶 𝑎𝑛𝑑∡𝐷𝑂𝐵
2x-8 + 4x BOF = 180 ∡
Adjacent angles on a line
Substitution
( 30) BOF = 180 ∡
(120) BOF = 180 ∡
BOF = 32 ∡

3. a = e, b=f, c=g,d=h
c=f , d=e
d+f=180 , c+e =180

4. Corresponding angles are congruent ( = )
48 𝑜
Corresponding angles are congruent ( = )

5. Same-side interior angles are supplementary
132 𝑜
Same-side interior angles are supplementary

6. Alternate Interior angles are congruent ( = )
48 𝑜
Alternate Interior angles are congruent ( = )

7. Alternate exterior angles are congruent ( = )
48 𝑜
Alternate exterior angles are congruent ( = )

8. Given line m and any point P not on m,
there exist exactly one line through P parallel to m
If line t is parallel to line d and line d is parallel to
line f, then line f is parallel to line t.

9. Draw line t through point P parallel to lines m and n
auxiliary line m t n
f = 35
and e = 41
so W = 76 P
Draw line t through point P parallel to lines m and n

10. 53 𝑜 53 𝑜 127 𝑜 Vertical angles theorem Same-side interior angles
Corresponding angles are
congruent ( = )
53 𝑜
Vertical angles theorem
53 𝑜
127 𝑜
Same-side interior angles
are supplementary

11. 145 𝑜 35 𝑜 Corresponding angles are congruent ( = )
Linear pair have a sum of 180

12. 54 𝑜 68 𝑜 Alternate Interior angles are congruent ( = )
𝟏𝟏𝟐 𝑜
68 𝑜
Corresponding angles are congruent ( = )
Linear pair have a sum of 180

13. 36+56=92 𝑜 36 𝑜 56 𝑜 Alternate Interior angles are congruent ( = )
Same-side Interior angles
are supplementary
Angle addition postulate

14. Same-side Interior angles
18 𝑜
82 𝑜
18+82=100 𝑜
Same-side Interior angles
are supplementary

15. 114 𝑜

16. 92 𝑜
42 𝑜
46 𝑜

17. 81 𝑜

18. 18 𝑜
94 𝑜

19. 46 𝑜

21. HOMEWORK

22. Triangle Angle Sum Theorem
180 𝑜
The sum of the 3 angle measures of any triangle is __________.
Triangle Angle Sum Theorem

23. exterior
angle

24. exterior
angle

25. exterior
angle

26. exterior
angle

27. exterior
angle

28. exterior
angle

29. NOT an
exterior
angle

30. NOT an
exterior
angle

31. remote interior angles
exterior
angle
non-adjacent or
remote interior angles

32. non-adjacent remote interior
In any triangle, the measure of the exterior angle is equal to the sum of the measures
of the ___________________angles.
These are also known as _______________________________angles.
non-adjacent
remote interior

33. Isosceles triangle theorem
Base angles of an
____________________
triangle are equal in measure.
isosceles
Isosceles triangle theorem

34. Equilateral triangle theorem
Each angle of an _________________ triangle
has a measure equal to 60°.
Equilateral triangle theorem

47. HOMEWORK