# 6th Grade - Complementary And Supplementary Angles

 Grade Level: 6th Skill: Geometry Topic: Complementary and Supplementary Angles Goal: Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Skill Description: Understand that complementary angles are two or more angles that equal 90 degrees. Supplementary angles are two or more angles that measure exactly 180 degrees. Use the definition of complementary and supplementary angles to find the measure of a missing angle. The sum of the measure of all three angles in every triangle will always be 180 degrees. Use this information to find the measure of a missing angle in a triangle.

## Building Blocks/Prerequisites

### Sample Problems

 (1) Angles m and n are complementary. If angle m = 60°, what is the measure of angle n? (30) (2) Angles s and t are supplementary. If angle t = 120°, what is the measure of angle s? (60) (3) A triangle has angles labeled a, b, and c, where a = 50° and b = 60°. What is the measure of angle c? (70) (4) In the figure below, angle VNL is 150°. What is the measure of angle LNB? (30) (5) If angle CMB has the measure of 110°, what are the angle measures of CMP, PMQ and BMQ? (CMP = 70, BMQ = 70, PMQ 110)

### Online Resources

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### Extra Help Problems

 (1) Angles x and y are complimentary. If angle x = 74°, what is the measure of angle y? (16) (2) Angles m and n are supplementary. If angle n = 162°, what is the measure of angle m? (18) (3) The angles of a triangle are w, x, and y, where y = 45° and x = 90°. What is the measure of angle w? (45) (4) Angle 1 compliments angle 2. If angle 1 measures 89°, what is the measure of angle 2? (1) (5) Angle Z supplements angle A. If angle A measures 136°, what is the measure of angle Z? (44) (6) A right triangle has an angle measuring 43°. What is the measure of the third angle? (47) (7) An equilateral triangle has 3 equivalent angle measures. What is the measure of each angle? Explain. (60) (8) If two angles measure 72° and 18°, what kind of angle pair are they? Explain. (complementary, together they measure 90) (9) An obtuse, isosceles triangle has angle 1 measuring 120° and angle 2 measuring 37°. What is the measure of the third angle? (23) (10) An acute isosceles triangle has angle X measuring 75° and angle y measuring 30°. What is the measure of the missing angle? (75) (11) Find the measure of the angle that complements 23°. (67) (12) Find the measure of the angle that supplements 117°. (63) (13) Looking at the figure, if x = 60 and y = 60, what is z equal to? (60) (14) Looking at the figure, if z = 60°, what is the measure of w? (120) (15) In the figure below, angle BEC is equal to 65°. Use this information to find the measure of angle AEB. (115) (16) If BEC is equal to 65° and angle AED is vertical to it, what is the measure of AED? Use the property of supplementary and vertical angles to find all four angle measures. (65) (17) In the figure below, if angle C = 120°, what is the measure of angle D? (60) (18) If the angle above A in the figure is 120°, what are the measures of angle A and B together? (180) (19) Use the properties of supplementary and vertical angles to find the measure of all angles in the figure below, if angle SBV is 48°. (ABG is 48, GBV is 132, SBA is 132) (20) In the figure, angle YXS is 45°. Use the properties of vertical supplementary and complementary angles to find the measures of angles YXS, SXQ, JXQ, and UXJ? (YXS-45, SXQ-135, JXQ-45, UXJ-90)