1. Angle-MANIA!
A- sauce
7/13/2010

2. Do Now
What the sum of the angles of any triangle?

3. Do Now
What the sum of the angles of any triangle? 40
180 70 70

4. Do Now How do we draw a line that is 180 degrees?
Take a couple seconds think about this.
180°

5. Objective Find the complements and supplements of angles
Identify and Find the angles of parallel lines and transversal
Find exterior angles of a triangle.
All of this will be done by solving equations

6. Purpose Learn some geometric terms
Develop your algebra and equations solving skills.

7. Relationships b/t Angles
If we know the relationships we can set up equations to solve for the measurement of angles we do not know.

8. Relationships b/t Angles
Supplementary Angles
sum of their angles is 180°
Example: 100° and 80° are supplementary.
We say, 100 ° is the supplement of 80 °
100°
80°

9. Relationships b/t Angles
Similarly, Complementary Angles
sum of their angles is 90°
Example: 35° and 55° are complementary.
We say, 35° is the complement of 55°
35°
55°

10. Finding the Supplement
Find the supplement of an angle measured as 45.
We subtract 45 number from 180 to find the supplement
X + 45 = 180
X = 180 − 45
X= ?
135°

11. Finding the Complement
Very similar to Finding the Supplement.
45 + X = 90
X = ?
45° is a Complement of itself.!!! 45
WHEWW!!

12. Find the measurement of angles
Solve for x
7x + 3x = 180
10x = 180
10x/10 = 180/10
X= 18
Use x to find the measurements
Without knowing these angles are supplementary would we have been able to find the measurement of these angles?
7x = 7 · 18 = 126
3x = 3 · 18 = 54
= 180

13. Pause. Complete Problems on Guided notes called
Find the supplement and complement of angle measured at 88 degrees.
Given ∠A and ∠B are supplementary and
m∠A = 7x + 4 & m∠B = 4x + 9. Find each angles measure.

14. Angles of Parallel Lines
First let’s consider a parallelogram

15. Angles of Parallel Lines
What’s this red line called?
Transversal

16. Transversal
Transversal is a line that intersects two or more lines that lie in the same plane in different points.
A transversal of parallel lines creates
Equal corresponding angles
Equal alternate interior angles
Supplementary interior angles on the same side of the transversal
Equal vertical angles

17. A A Corresponding Angles
Corresponding Angles are in the same position around both lines. A

18. Alternate Interior Angles
We can easily see that the angles are inside (between) the
parallel lines. Why alternate? A

19. Interior angles on the same side
Also called consecutive interior angles Why are they supplementary? A A

20. A A Vertical Angles Vertical angles are opposite of one another.
What is another pair of vertical angles?

21. Identify Relationship b/t angles
Angle 2 and Angle 6
Consecutive Angles
Angle 4 and Angle 5
Corresponding Angles
Angle 1 and Angle 6
Alternate Interior Angles
Angle 5 and Angle 8
Vertical Angles

22. Find the measurement of angles
Angle 1 = 56°, because vertical angle
Angle 2= = 124°, supplementary
In partners, find the measurement of the rest of the angles and why.
Angle 3 = 124 °
Angle 4 = 56°
Angle 5 = 124°
Angle 6 = 124°
Angle 7 = 56°

23. Solve for variables
x equals 108 because it’s the supplement of 72 AND?
y = 36 because 3y and x are corresponding angles.
3y = 108
y = 36
(3z + 18) is equal to 108 degrees. Why?
What is z?

24. Pause Practice Problems
Find the value of x and y. (Hint: Extend lines to determine transversal)
If < 2 = 35°, find the measure of the rest of the angles

25. Exterior Angles of Triangle
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
SO w = x + y
What other relations do we know?

26. Find the exterior angle
First we notice this is an isosceles triangle.
We also need to find
measure of base angles
So we can use this equation:
44 + 2y = 180
Why? Y

27. Find the exterior angle
44 + 2y = 180 (subtract 44 from both sides)
2y = 136 (divide both sides by 2)
y = 68
So now we can find x because?

28. Find the exterior angle
X = = 112 because x is an exterior angle of the triangle .

29. Pause
Practice Problem.
Find x.

30. Proof of Triangle Theorem
Sum of angles in triangle equal to 180°

31. Proof of Triangle Theorem
Next we draw parallel to base ‘a’ through point P (intersection of ‘c’ and ‘b’)
First, lets label the sides and angles A b c C B a