ANgle Relationship.pptx

Math7 angle relationships k12

1. MS. JERALDEL M. ENCEPTO 7TH GRADE Mathematics 7 ANGLE PAIRS ANGLE PAIRS

2. Complementary Angles Supplementary Angles Adjacent Angles ANGLE PAIRS Vertical Angles Linear Pair Congruent Angles

3. Direction: Identify the kinds of angle pairs. 1. ∠JAT and TAH— ∠JAE and HAT— ∠MAT and TAH— ∠EAM and MAT--- 5. ∠JAE and MAT--

4. Direction: Identify the kinds of angle pairs. ∠JAT and TAH— ∠JAE and HAT--- ∠MAT and TAH— ∠EAM and MAT- -- ∠JAE and MAT- - SA, LP, AA VA CA,AA SA, LP, AA CA

5. State whether the statement is always true (AT), sometimes true (ST) or never true (NT). ____1. Angles with a common side and vertex but no interior points are adjacent. ____2. The supplement of an angle is acute. ____3. The complement of an angle is obtuse. ____4. The complement of any acute angle is acute. ____5. Two intersecting lines form two pairs of vertical angles. ____6. Two supplementary angles are congruent. ____7. Angles that form a linear pair are supplementary. ____8. Supplementary Angles form a linear pair. ____9. Two adjacent angles form a linear pair. ____10. Complements of congruent angles are congruent.

6. State whether the statement is always true (AT), sometimes true (ST) or never true (NT). ____1. Angles with a common side and vertex but no interior points are adjacent. ____2. The supplement of an angle is acute. ____3. The complement of an angle is obtuse. ____4. The complement of any acute angle is acute. ____5. Two intersecting lines form two pairs of vertical angles. ____6. Two supplementary angles are congruent. ____7. Angles that form a linear pair are supplementary. ____8. Supplementary Angles form a linear pair. ____9. Two adjacent angles form a linear pair. ____10. Complements of congruent angles are congruent. AT ST NT AT AT ST AT ST ST AT

7. A nswer me!

8. Identify whether the following pairs of angles are ADJACENT ANGLES, LINEAR PAIRS, COMPLEMENTARY ANGLES , SUPPLEMENTARY ANGLES or VERTICAL ANGLES. Refer to the given figure. 1. ∠𝐷𝑂𝐸 and ∠𝐸𝑂𝐴 = ______________________________ 2. ∠𝐴𝑂𝐵 and ∠𝐴𝑂𝐸 = ______________________________ 3. ∠𝐸𝑂𝐷 and ∠𝐷𝑂𝐶 = ______________________________ 4. ∠𝐸𝑂𝐷 and ∠𝐵𝑂𝐷 = ______________________________ 5. ∠𝐷𝑂𝐸 and ∠𝐵𝑂𝐴 = ______________________________ A B C D E O LINEAR PAIRS, ADJACENT ANGLES, SUPPLEMENTARY ANGLES LINEAR PAIRS, ADJACENT ANGLES, SUPPLEMENTARY ANGLES ADJACENT ANGLES, COMPLEMENTARY ANGLES LINEAR PAIRS, ADJACENT ANGLES, SUPPLEMENTARY ANGLES VERTICAL ANGLES

9. MS. JERALDEL M. ENCEPTO Math Teacher 7TH GRADE Mathematics 7 ANGLE PAIR RELATIONSHIP

10. 1. Identify and determine the measure of angles a. supplementary angles b. complementary angles c. congruent angles d. adjacent angles e. linear pair f. vertical angles 2. Derive relationships of geometric figures using measurements and by inductive reasoning. LEARNING OBJECTIVES:

11. 1. Find the complement and supplement of an angle whose measure is: COMPLEMENTARY AND SUPPLEMENTARY ANGLE a. 65 o b. 45 o 14’ c. 34 o 25’36” Note: 1 o = 60’ 1’=60” Angle Complement Supplement 65 o 45 o 14’ 34 o 25’36” b. 45 o 14’ 90 o 60’ -45 o 14’ 89 o / 44 o 46’ 180 o 60’ -45 o 14’ 179 o / 134 o 46’ c. 3 4 o 25’36” 90 o 59’60” -34 o 25’36” 89 o / 55 o 34’24” 180 o 59’60” - 34 o 25’36” 179 o / 145 o 34’24” 25 o 115 o 44 o 46 134 o 46’ 55 o 34’24” 145 o 34’24” degrees (°), minutes ('), seconds (")

12. 2. Solve for the value of x. 37.5 o x + x + 15= 90 2x+15= 90 2x=90-15 2x= 75 x=37.5 COMPLEMENTARY AND SUPPLEMENTARY ANGLE 52.5 o x x + 15 51 o 39 o 2x + 5 3x 125 o 55 o 2x -15 4x-15 2x + 5 + 3x= 90 5x+5= 90 5x=90-5 5x= 85 x=17 4x - 15 + 2x-15 = 180 6x-30= 180 6x=180+30 6x= 210 x=35

13. 3. The measure of the complement of an angle is twice the measure of the angle. What is the measure of the angle? What is the measure of its complement? 90 o –x = 2x 90 o = 2x + x 90 o = 3x 30 o = x x= 30 o COMPLEMENTARY AND SUPPLEMENTARY ANGLE Let : x= measure of the angle 90- x= the measure of its complement 4. The measure of an angle is 30 o more than twice the measure of its supplement. Find the measure of the angle and its supplement? x = 2(180 o – x) + 30 o x= 360 o - 2x + 30 o x+ 2x = 360 o + 30 o 3x= 390 o x= 130 o Let : x= measure of the angle 180- x= the measure of its supplement 30 o 60 o 130 o 50 o

14. A n swer the following questions. m∠AEC + m∠CED = 180 o 2x + 3 + x = 180 o 3x = 180 o – 3 3x = 177 o x = 59 o = ∠CED ADJACENT ANGLES AND LINEAR PAIR Are ∠1 and ∠ 2 adjacent angles? Are ∠1 and ∠ 3 adjacent angles? Are ∠3 and ∠ 2 adjacent angles? Do ∠1 and ∠ 2 form a linear pair? Do ∠1 and ∠ 2 adjacent angles? Name a pair of adjacent angles that are complementary. Name two angles that have the same measure and form a linear pair. ∠AEC and ∠CED form a linear pair. The measure of ∠AEC is the three degrees more than twice the measure of ∠CED. Find ∠AEC. No Yes No Yes Yes ∠BEC and ∠CED ∠BEC and ∠BED ∠2 and ∠3 A B C D 3 E x = ∠CED 2x + 3= ∠AEC 2(59 o ) + 3 = ∠CED 121 o = ∠AEC 1 2

15. 1. ∠3 and ∠4 are vertical angles. If m ∠3= 4x + 7 and m∠4 = 5x – 8 , find the measure of the two angles. ∠3 ≅ ∠4 m∠3 = m ∠4 4x + 7= 5x-8 4x-5x= -8-7 -x = -15 x=15 CONGRUENT AND VERTICAL ANGLES 67 o 67 o 5x - 8 4x - 7 Vertical angles are congruent. m∠3 = 4x +7 m∠3 = 4( 15 ) + 8 m∠3 = 60 + 7 m∠3 = 67 m∠4 = 5x -8 m∠4 = 5( 15 ) - 8 m∠4 = 75 - 8 m∠4 = 67

16. 2. ∠5 and ∠6 are vertical angles. If m ∠5= 6x and m∠6 = 4x + 6 , find the measure of the two angles. ∠5 ≅ ∠6 m∠5 = m ∠6 6x = 4x + 6 6x-4x= 6 2x = 6 x=3 CONGRUENT AND VERTICAL ANGLES 18 o 18 o 4x + 6 6x Vertical angles are congruent. m∠5= 6x m∠5 = 6( 3 ) m∠5 = 18 m∠6 = 4x + 6 m∠6 = 4( 3 ) + 6 m∠6 = 12 + 6 m∠6 = 18 ANGLE PAIR RELATIONSHIP

17. ANGLE PAIR RELATIONSHIP 1. Vertical angles are congruent. 2. If two angles form a linear pair, then they are supplementary. 3. The sum of complementary angles is 90 o . 4. The sum of supplementary angles is 180 o .

18. Let’s Try!

19. Given: ∠1 and ∠ 2 are supplementary angles. If m∠1 = 2x +10 and m∠5 = 5x +30; 1. Find the value of x. m ∠1+ m ∠5 =180 2x +10 +5x+30= 180 7x +40 = 180 7x = 180- 40 7x= 140 X=20 2. m ∠1= 9. m ∠8= 3. m ∠2= 10. m ∠9= 4. m ∠3= 11. m ∠10= 5. m ∠4= 12. m ∠11= 6. m ∠5= 13. m ∠12= 7. m ∠6= 8. m ∠7= 1 2 3 8 7 6 5 4 9 10 11 12 180 o

20. Find the value of x in each figure. Copy on a separate sheet of paper and complete the answer in the table. 1. (2x + 11) o (3x - 45) o 2. (2x - 5) o (4x - 7) o 3. (x - 20) o (3x + 6) o 2𝑥 + 11 = 3𝑥 − 45 (2𝑥 − 5) + (4𝑥 − 7) = 180 (𝑥 − 20) + (3𝑥 + 6) = 90

21. Refer to the given figure. 1. Give another name for ∠𝟏. 2. Name all angles with AF as a side. 3. Determine how many acute angles there are with point A as their vertex. Name two of these acute angles.

22. GREAT WORK!