Adjacent, vertical, complementary and supplementary angles Mr. Peterson

CC standard 7.g.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simples equations for an unknown angle in a figure. Paraphrase: Identify adjacent and vertical angels. Find angel measures using adjacent and vertical angles. Classify pairs of angles as complementary, supplementary, or neither. Find angle measures using complementary and supplementary angles.

Input Vertex - Endpoint where two line segments or lines come together. Adjacent angles – Angles that share a common side and have the same vertex. Vertical angles – Opposite angles formed by the intersection of two lines. Congruent angles – Angles that have the same measure. Complementary angles – Two angles whose sum of their measure is 90°. Supplementary angles - Two angles whose sum of their measure is 180°.

Angles that measure less than 90°. Acute - Angles that Types of Angles Angles that measure less than 90°. Acute - Angles that measure more than 90° and less than 180°. Obtuse - Right - Angles that measure exactly 90°. Straight - Angles that measure exactly 180°.

Adjacent angles are “side by side” and share a common ray. 15º 45º

These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

When 2 lines intersect, they make vertical angles. 75º 105º 105º 75º

Vertical angles are opposite one another. 75º 105º 105º 75º

Vertical angles are opposite one another. 75º 105º 105º 75º

Vertical angles are congruent (equal). 150º 30º 150º 30º

Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Angles but not Adjacent

Guided Practice Directions: Identify each pair of angles as vertical, supplementary, complementary, or none of the above.

#1 120º 60º

#1 120º 60º Supplementary Angles

#2 60º 30º

#2 60º 30º Complementary Angles

#3 75º 75º

#3 Vertical Angles 75º 75º

#4 60º 40º

#4 60º 40º None of the above

#5 60º 60º

#5 60º 60º Vertical Angles

#6 135º 45º

#6 135º 45º Supplementary Angles

#7 25º 65º

#7 25º 65º Complementary Angles

#8 90º 50º

#8 90º 50º None of the above

Protractor work: Guided Practice 1. Draw a straight line. 10 170 20 160 150 30 140 40 130 50 120 60 110 70 100 80 90

Protractor work: Guided Practice 2. Draw a ray to form an angle of 40°from the right side. 10 170 20 160 150 30 140 40 130 50 120 60 110 70 100 80 90

Protractor work: Guided Practice 3. Find the measure of the angle supplementary to the angle you just created. 140° 40°

Protractor work: Guided Practice 4. Use a straightedge to extend the ray you drew to below the line. 140° 40°

Protractor work: Guided Practice 5. What is the measure of angle X? 140° 40° x y 40° 140° Why? Angle Y? How did you find the answer?

Time for you to try some on your own