Angle Relationships OBJ: To ID and use adjacent, vertical, complementary, supplementary, and linear pairs of angles, and perpendicular lines To determine what info can and cannot be assumed in a picture

Angle Relationships Adjacent angles- V Y Z X W Adjacent angles- Angles with a common ray and vertex, but have no common interior pts Vertical angles- 2 non-adjacent angles formed by 2 intersecting lines Vertical Angles are congruent

Angle Relationships Continued V Y Z X W Linear pairs: Adjacent angles whose non-common sides are opposite rays Supplementary angles- 2 angles whose sum is 180 degrees

Angle Relationships continued Perpendicular lines- Lines that intersect to form a 90 degree angle Complementary angles- 2 angles whose sum is 90 degrees

Example: Find x and 9x – 4 + 4x – 11 = 180 13x – 15 = 180 13x = 195 G K H J I 9x - 4 4x - 11 Find x and 9x – 4 + 4x – 11 = 180 13x – 15 = 180 13x = 195 X = 15 9 ( 15 ) – 4 = ? 135 – 4 = 131

Your Turn: Find x and 13x + 7 = 16x - 20 27 = 3x 13 ( 9 ) + 7 = 124 E A B C D 16x - 20 13x + 7 Find x and 13x + 7 = 16x - 20 27 = 3x 13 ( 9 ) + 7 = 124 9 = x 180-124 = 56

Example The measure of the supplement of an angle is 60 less than 3 times the measure of the complement of the angle. Find the measure of the angle. Let x = angle The measure of the supplement is 60 less than 3 times the complement 180 – x 3 ( 90 – x ) – 60 = 180 – x = 270 – 3x -60 2x = 30 180 + 2x = 210 x = 15

Your Turn: The measure of the complement of an angle is 3.5 times smaller than the measure of the supplement angle. Find the measure of the angle. 3.5 ( 90 – x ) = 180 - x Solve for x. X = 54

What Can Be Assumed? Open your book to page 38. Read through the chart. Let’s discuss anything you do not understand

Homework Put this in your agenda Pg 39 3 - 43 odd