Find the measure of the angle indicated... please help

Step-by-step explanation:

41). Measure of an external angle of a triangle is equal to the sum of teh opposite two angles.

140° = (13x + 9)° + (5x + 5)°

140 = 18x + 14

18x = 140 - 14

18x = 126

x = 7

m∠R = (13x + 9)

        = 13×7 + 9

        = 100°

42). m∠DCA = m∠E + m∠D

126° = (6x + 2)° + (5x + 3)°

126 = 11x + 5

11x = 126 - 5

11x = 121

x = 11

m∠D = (5x + 3)

         = 5(11) + 3

         = 58°

43). m∠DPQ = m∠Q + m∠R

11x + 3 = 70° + (x + 13)°

11x + 3 = x + 83

11x - x = 83 - 3

10x = 80

x = 8

m∠R = (x + 13)

        = 21°      

44). m∠QST = m∠T + m∠U

13 + 13x = 100 + (3x + 3)

13 + 13x = 3x + 103

13x - 3x = 103 - 13

10x = 90

x = 9

m∠U = 3x + 3

        = 3(9) + 3

        = 27 + 3

        = 30°

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