Answer:
C = 145.4°
By creating a system of equations (2 equations) with the information from a problem, we can substitute and solve for the missing variables.
Step-by-step explanation:
Linear pairs are found on a straight line, so they total to 180°.
C + D = 180 ......eq'n [1]
C is seven more than four times D can be represented with this equation:
C = 4D + 7 ........eq'n [2]
We can solve by substituting [2] into [1], replacing "C".
C + D = 180
4D + 7 + D = 180
Collect like terms
5D + 7 = 180
Subtract 7 from both sides
5D = 173
Divide both sides by 5
D = 173/5
As a decimal, D = 34.6°.
Using eq'n [2], find C. Substitute the value of "D". Solve.
C = 4D + 7
C = 4(173/5) + 7
C = (692/5) + 7
C = (692/5) + (35/5) Find a common denominator.
C = (692+35)/5 Combine into numerator.
C = 727/5
As a decimal, C = 145.4°.
