the measure of an angel and its complement are given. Determine the measures of the two angles. b. ×+5+3×-1

Question

I need help  

Answer 1

To approach this problem we first need to understand what, exactly, a complementary angle is.  The term complementary angle simply means that 2 angles adjacent to one another's sum is 90˚.  Judging from the text of your question I am concluding that the 2 angles are derived as follows:

 

Angle A = (X + 5)

Angle B = (3X - 1)

 

Using this information, we can calculate the value of X and thus calculate the values of both angles A and B

 

First, since we know that angles A and B are complementary we know that the sum of these angles must be 90˚.  Therefore we can set angles A and B equal to 90˚ ((X + 5)˚ + (3X - 1)˚=90)

 

Simplify by combining like terms 4X +4 = 90˚

 

Solve for X - 4X + 4 = 90˚

                         - 4    - 4

                   4X       = 86˚

Divide by 4 on both sides---X = 86/4; X = 21.5

 

Substitute to verify

Angle A = (21.5)+5 = 26.5˚

Angle B = 3(21.5) -1

                   64.5 - 1 = 63.5

Angle A = 26.5˚

Angle B = 63.5˚

 

63.5˚ + 26.5˚ = 90˚