Presentation Transcript
Slide 1:Algebra and Geometry Using Angle Relationships
Slide 2:What do we know about 3x complementary angles?
x + 10 You could write this equation:
(3x) + (x+ 10) = 90 Complementary Angles Their sum is 90º.
Slide 3:Let’s solve for x:
3x + x + 10 = 90
4x + 10 = 90
-10 -10
4x = 80
4 4
x = 20 If x = 20, then
3x = 3(20) = 60º
and
x + 10 = 20 + 10 = 30º
Check:
60 + 30 = 90
Yes, you need to find each angle and yes, you should double check that your answer makes sense.
Slide 4:What do we know about supplementary angles? Supplementary angles add up to 180º Write an equation you could use to solve for x in this problem. 4x + x + 30 = 180 Supplementary Angles
Slide 5:4x + x + 30 = 180
5x + 30 = 180
-30 -30
5x = 150
x = 30 Now find the measure for each angle: 4x = 4(30) = 120º
x + 30 = 30 + 30 = 60º
120 + 60 = 180, so that works! 4x x + 30
Slide 6:Vertical angles are congruent. How will that help us set up and equation? Congruent means the same so the angles are equal.
4x + 40 = 9x - 10 4x + 40 9x - 10 Vertical
Angles
Slide 7:4x + 40 = 9x – 10
-4x -4x___
40 = 5x - 10
+10 + 10
50 = 5x
10 = x
Find each angle.
They should be the same. 4x + 40
4(10) + 40
40 + 40
80º 9x - 10
9(10) – 10
90 - 10
80º 80 80
Slide 8:Alternate Interior Angles are congruent, too. 2x + 20
4x - 10 2x + 20 = 4x – 10
-2x -2x
20 = 2x – 10
+10 +10
30 = 2x
15 = x 2x + 20 4x – 10
2(15) + 20 4(15) – 10
30 + 20 60 – 10
50º 50º Alternate Angles
Slide 9:Alternate Exterior Angles are also congruent. 6x
4x + 40 6x = 4x + 40
-4x -4x
2x = 40
x = 20 6x 4x + 40
6(20) 4(20) + 40
º 80 + 40
120º
Slide 10:Corresponding Angles are congruent, too! 2x + 10
x + 35 2x + 10 = 1x + 35
-1x -1x
1x + 10 = 35
- 10 -10
x = 25 2x + 10 x + 35
2(25) + 10 25 + 35
50 + 10 60º
60º Corresponding Angles
Slide 11:In summary…..
Complementary angles add up to 90 (corner)
Supplementary angles add up to 180 (straight)
In all the others the angles are congruent, including
Vertical angles X
Alternate interior angles Z
Corresponding angles F
Alternate exterior angles