Angles Relationships Unit 7 Math 7

Angle Relationships – Warm UP Find the measure of angle 1 if the measure of angle 4 = 135o Angles 1 and 4 are _______________ angles. If they are supplementary angles, they must add up to _________degrees.

Angle Relationships Let’s Review… Adjacent Angles: two angles that share a vertex and a side but no points in their interiors. Vertical Angles: angles formed by two intersecting lines, and are opposite each other. Vertical angles are congruent. Congruent Angles: angles that have the same measure

Angle Relationships Supplementary Angles: two angles whose measures add to 180° Complementary Angles: two angles whose measures add to 90°

Angle Relationships Example 2: Find the measure of angles 2, 3, and 4 if 1 = 43o Angles 1 and 2 are _______________ angles. If they are supplementary angles, they must add up to 180 degrees. Angle 2 measures 137 degrees. supplementary

Angle Relationships Example 3 – Find the measure of each angle Angle HPM – 108 degrees Angle JPI – 38 degrees

Angle Relationships Example 3 – Find the measure of each angle Angle IPH – 34 degrees Angle KPL –

Let’s Review Packet from Last week

EQ: How can we find missing angles using rules of geometry?

Find the complement of... 1) 20 70 2) 47 43 No complement 3) 100

Find the supplement of the given angle. 1) 40 140 5) 89 91 2) 18 162 6) 23 157 3) 153 27 7) 131 49 4) 65 115 8) 118 62

The easiest way to find the missing measure(s) of an angle is to set up an equation and solve. For example:

Complementary Angles sum is 90 . b a x+ 40 = 90 - 40 -40 x 40 x = 50 - Angles whose sum is 90 . b a x+ 40 = 90 - 40 -40 x 40 x = 50

Supplementary Angles - Angles whose sum is 180o Find the value of x. 30 x + 30 = 180 - 30 - 30 x = 150

(Guided Practice) Write a variable equation and solve. Find an angle whose supplement is 30 less than twice the angle. x 2x - 30 x + (2x - 30) = 180 3x - 30 = 180 +30 +30 3x = 210 70 x = 70

Write a variable equation and solve. Find an angle whose complement is 20 more than three times the angle. x + 3x + 20 = 90 x 4x + 20 = 90 3x + 20 - 20 -20 4x = 70 4 4 x = 17.5

Vertical Angles Theorem - the opposite angles of intersecting lines must be equal.

What’s the relationship between angles a and b? Vertical Angles Theorem - the opposite angles of intersecting lines must be equal. Find the missing angles a, b and c. What’s the relationship between angles a and b? 25 155 b c a 155 25

Summary Name some ways in which we can find the missing measure of an angle?

Independent Practice/HW