Complementary and Supplementary Angles Warm-up and Instruction.

Angle4 and Angle5 are complements, and Angle1 and Angle5 are complements. 3 lines intersect and form 6 angles. Counter-clockwise, from top left, the angles are 1, 2, 3, 4, 5, right angle. By the congruent complements theorem, which angle is congruent to Angle4?

a. 1

3 lines are shown. A line with points B, A, E intersects a line with points C, A, F at point A. A line extends from point A to point D in between angle E A F. Which are linear pairs?

a. BAC and CAE c. CAE and FAE

"Try it" interactive instruction: Proving the Congruent Supplements Theorem.

(1.) statement: ∠3 and ∠4 are supp. (1.) reason: given (2.) statement: ∠1 and ∠2 are supp. (2.) reason: given (3.) statement: ∠1 ≅ ∠4 (3.) reason: given (4.) statement: m∠1 = m∠4 (4.) reason: def. of ≅ angles (5.) statement: m∠1 + m∠2 = 180 (5.) reason: def. of supp. angles (6.) statement: m∠3 + m∠4 = 180 (6.) reason: def. of supp. angles (7.) statement: m∠1 + m∠2 = m∠3 + m∠4 (7.) reason: substitution property (8.) statement: m∠1 + m∠2 = m∠3 + m∠1 (8.) reason: substitution property (9.) statement: m∠2 = m∠3 (9.) reason: subtraction property (10.) statement: ∠2 ≅∠3 (10.) reason: def. of ≅ angles

Given: ∠1 and ∠2 are complements, ∠2 and ∠3 are complements, and m∠1 = 35°. Prove: m∠3 = 35° 4 lines extend from a point and form 3 angles. The angles are labeled 1, 2, 3 from left to right. Complete the missing parts of the paragraph proof.

By the ✔ congruent complements theorem ✔, we know that angle 1 is congruent to angle 3. The measure of angle 1 equals the measure of angle 3 by the definition of ✔congruent✔ right angles. Then, using the ✔ substitution property✔, the measure of angle 3 is ✔ 35 ✔ degrees.

Which pair of angles is complementary? 2 angles are shown. One angle is 69 degrees and the other is 31 degrees. 2 right angles are shown. 2 angles are shown. One angle is 56 degrees and the other is 34 degrees.

c. (The last pair. They're labeled 56 and 34 degrees)

3 lines are shown. A line with points C, A, F intersects a line with points E, A, B at point A. A line extends from point A to point D in between angle E A F. Angle C A E is 61 degrees, angle D A F is 90 degrees, and angle F A B is 61 degrees. Find the following angle measures.

mEAD = 29 degrees & mCAB = 119 degrees

A horizontal line has points J, K, L. A line extends from point K up and to the right to point M. Angle J K M is (10 y + 6) degrees and angle M K L is (8 y minus 6) degrees What is the value of y?

y = 10 & mJKM = 106 degrees & mMKL = 74 degrees