1. Warm Up

3. Angle Relationships Objective:
Students will identify and use special pairs of angles and perpendicular lines.

4. Adjacent Angles
Adjacent angles are two angles that lie in the same plane, have a common vertex, and a common side, but no common interior point. 1 2 3 4

5. Vertical Angles
Vertical angles are two nonadjacent angles formed by two intersecting lines
Vertical angles are ALWAYS congruent 4 3 1 2
Angles 1 and 3 are vertical;
Angles 2 and 4 are vertical.

6. Linear Pair
A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.
Linear pairs have a sum of 180 degrees. 2 1
Angles 1 and 2 form a linear pair

7. Complementary Angles
Complementary angles are 2 angles whose measures have a sum of 90 degrees
Complementary angles can be adjacent or nonadjacent
200
700

8. Supplementary Angles
Supplementary angles are 2 angles whose measures have a sum of 180 degrees.
Supplementary angles can be adjacent or nonadjacent.
520
1280

9. Perpendicular Lines
Perpendicular lines intersect to form 4 right angles
Perpendicular lines intersect to form congruent adjacent angles
Segments and rays can be perpendicular to lines or other segments and rays
The right angle symbol in the figure indicates the lines are perpendicular

10. Examples Lines p and q intersect to form adjacent angles 1 and 2.
If m<1 = -3x+18 and m<2 = 8y-70, find the values of x and y so that p is perpendicular to q.
The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 and 2 form a linear pair, what are their measures?
X = -24, y = 20
37, 143

11. Examples, continued…
If m<A = 75, what are the complement and supplement of <A?
m<B = x. Name the complement and supplement of <B.
The supplement of an angle is twice the measure of the angle. Find the angle and its supplement.
The difference between the measures of 2 supplementary angles is 42 degrees. Find the angles.
A supplement of an angle is 6 times as large as the complement of the same angle. Find the angles.
C = 15, S = 105
C = 90-x, S = 180-x
60, 120
69, 111
72, C = 18, S = 108