ssrs barcode font free Supplementary angles: Supplementary angles are two angles whose measures total 180 . in Objective-C

Print Denso QR Bar Code in Objective-C Supplementary angles: Supplementary angles are two angles whose measures total 180 .

4. Supplementary angles: Supplementary angles are two angles whose measures total 180 .
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Thus, in Fig. 1-41(a) the angles of a and b are adjacent supplementary angles. However, in Fig. 1-41(b) the supb 180 . Either of two supplementary angles is said to be plementary angles are nonadjacent. In each case, a the supplement of the other.
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CHAPTER 1 Lines, Angles, and Triangles
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1.7B Principles of Pairs of Angles
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PRINCIPLE 1:
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If an angle of c is cut into two adjacent angles of a and b , then a
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25 and b 35 in Fig. 1-42, then c 25 35 60 .
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Fig. 1-42
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Fig. 1-43
Vertical angles are congruent.
Thus if AB and CD are straight lines in Fig. 1-43, then /1 > /3 and /2 > /4. Hence, if m/1 40 ; in such a case, m/2 m/4 140 .
PRINCIPLE 3:
40 , then m/3
If two complementary angles contain a and b , then a
40 , then b
Thus if angles of a and b are complementary and a
PRINCIPLE 4:
50 [Fig. 1-44(a) or (b)].
Adjacent angles are complementary if their exterior sides are perpendicular to each other.
Fig. 1-44
Thus in Fig. 1-44(a), a and b are complementary since their exterior sides AB and BC are perpendicular to each other.
PRINCIPLE
If two supplementary angles contain a and b , then a
140 , then b
Thus if angles of a and b are supplementary and a
PRINCIPLE
40 [Fig. 1-45(a) or (b)].
Adjacent angles are supplementary if their exterior sides lie in the same straight line.
Thus in Fig. 1-45(a) a and b are supplementary angles since their exterior sides AB and BC lie in the same straight S line AC .
Fig. 1-45
PRINCIPLE
Fig. 1-46
If supplementary angles are congruent, each of them is a right angle. (Equal supplementary angles are right angles.)
Thus if /1 and /2 in Fig. 1-46 are both congruent and supplementary, then each of them is a right angle.
CHAPTER 1 Lines, Angles, and Triangles
SOLVED PROBLEMS
1.13 Naming pairs of angles (a) In Fig. 1-47(a), name two pairs of supplementary angles. (b) In Fig. 1-47(b), name two pairs of complementary angles. (c) In Fig. 1-47(c), name two pairs of vertical angles.
Fig. 1-47
Solutions
(a) Since their sum is 180 , the supplementary angles are (1) /1 and /BED; (2) /3 and /AEC. (b) Since their sum is 90 , the complementary angles are (1) /4 and /FJH; (2) /6 and /EJG. (c) Since KL and MN are intersecting lines, the vertical angles are (1) /8 and /10; (2) /9 and /MOK.
1.14 Finding pairs of angles Find two angles such that: (a) The angles are supplementary and the larger is twice the smaller. (b) The angles are complementary and the larger is 20 more than the smaller. (c) The angles are adjacent and form an angle of 120 . The larger is 20 less than three times the smaller. (d) The angles are vertical and complementary.
Solutions
In each solution, x is a number only. This number indicates the number of degrees contained in the angle. Hence, if x 60, the angle measures 60 . (a) Let x m (smaller angle) and 2x m (larger angle), as in Fig. 1-48(a). Principle 5: x 2x 180, so 3x 180; x 60. 2x 120. Ans. 60 and 120 (b) Let x m (smaller angle) and x 20 m (larger angle), as in Fig. 1-48(b). Principle 3: x (x 20) 90, or 2x 20 90; x 35. x 20 55. Ans. 35 and 55 (c) Let x m (smaller angle) and 3x 20 m (larger angle) as in Fig. 1-48(c). Principle 1: x (3x 20) 120, or 4x 20 120; x 35. 3x 20 85. Ans. 35 and 85 (d) Let x m (each vertical angle), as in Fig. 1-48(d). They are congruent by Principle 2. Principle 3: x x 90 , or 2x 90; x 45. Ans. 45 each.
Fig. 1-48
CHAPTER 1 Lines, Angles, and Triangles
1.15 Finding a pair of angles using two unknowns For each of the following, be represented by a and b. Obtain two equations for each case, and then find the angles. (a) The angles are adjacent, forming an angle of 88 . One is 36 more than the other. (b) The angles are complementary. One is twice as large as the other. (c) The angles are supplementary. One is 60 less than twice the other. (d) The angles are supplementary. The difference of the angles is 24 .
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