Understanding Angle Measurements: Complementary, Supplementary, and More
This guide explores essential angle measurements in geometry, defining key types such as complementary angles (adding to 90°), supplementary angles (adding to 180°), perpendicular angles (90°), vertical angles (equal measures), straight angles (180°), and adjacent angles (next to each other). Through practical examples, you will learn how to find unknown angles using subtraction from 90° and 180°, enhancing your understanding of angle relationships in various geometric scenarios. Perfect for students and anyone interested in mastering angle concepts.
Understanding Angle Measurements: Complementary, Supplementary, and More
E N D
Presentation Transcript
Vocabulary Words • Complement(ary) Angles – 2 angles that add up to 90°. • Supplement(ary) Angles – 2 angles that add up to 180°. • Perpendicular Angles – A type of angle that contains a 90° angle. • Vertical Angles – Opposite angles that have the same (or equal) degree measure. • Straight Angles – A straight line that measures 180°. • Adjacent Angles – Angles that are next to or beside each other.
Example C 74° A B D If the measure of angle CBD is 74°, what is the measure of angle ABC? Notice that the two angles together make up angle ABD which is a straight angle. So the two angles added together equal 180°. Since we know one angle is 74°, just subtract 74 from 180 (180 – 74) and we get 106. So the measure of ABC = 106°.
Two Lines Cut by a Transversal 1 2 3 4 5 6 7 8 If the measure of angle 4 = 127°, what is the measure of angle 7? Notice that 4 is the bottom right angle. Notice that 8 is the bottom right angle. Since they have the same position, their angle measures are the same. So, angle 8 = 127°. Angles 7 and 8 are adjacent to each other and together they make a straight angle which adds up to 180°. To find angle 7 subtract 127 from 180 (180 – 127) and we get 53. So, angle 7 = 53°.
Vertical Angles 1 2 4 3 If the measure of angle 2 is 95°, what is the measure of angles 3 and 4? Angles 2 and 3 are adjacent and together they make a straight angle. Once again, just subtract 95 from 180 (180 – 95) and we get 85. So, angle 3 = 85°. Angles 2 and 4 are vertical angles. Recall they are opposite angles that have the same angle measure. Since angle 2 is 95°, then angle 4 is 95°.
SAMPLE ARMT QUESTION • In the figure below, lines a, b, and c intersect and form the angles shown. • If the measure of angle 9 = 42° and angle 5 and angle 6 are complementary, what is the measure, in degrees, of angle 5? b a c 5 6 4 7 9 8
Sample ARMT Question Cont. • Notice that angles 6 and 9 are vertical angles. If angle 9 is 42 degrees then angle 6 is 42 degrees. • Since angles 5 and 6 are complementary, they add up to 90 degrees. To find the measure of angle 5 just subtract 42 from 90 and we get 48 degrees. • Thus, the measure of angle 5 is 48 degrees.
Complementary and Supplementary Angles • If the measure of one angle is 49°,what is the measure of its complement? • Just subtract 49 from 90 (90 – 49) and we get 41. So the complement is 41°. • Its supplement? • Just subtract 49 from 180 (180 – 49) and we get 131. So the supplement is 131°.
