Angle A is the complement of angle B and the supplement of angle C . The measure of angle C is 106 degrees. What is the degree measure of angle B?

Answers

Given:

m∠C = 106
m∠B = ?

Solution:

m∠A + m∠C = 180   ⇒ Supplementary angles have a sum of 180.
m∠A + 106 = 180
m∠A + 106 - 106 = 180 -106
m∠A = 74

m∠A + m∠B = 90     ⇒ Complementary angles have a sum of 90.
74 + m∠B = 90
74 - 74 + m∠B = 90 - 74
m∠B = 16

The measure of angle B is 16.

^_^

Step-by-step explanation:

  A = 90-B           /  A is the complement of  B

  A  =   180-C      / A is the supplement of  C

  A  =    180- 106   =  74

   74  =   90-B

     B  =   16 degrees



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