Angle QRS is a straight angle, so a+b+c+d = 180. If a=2c, c=2b, and b=d/3, what are the values of a,b,c,and d?

Question

Angle QRS is a straight angle, so a+b+c+d = 180.  If a=2c, c=2b, and b=d/3, what are the values of a,b,c,and d?

drwls · Answer

You have 4 equations in 4 unknowns. Use substitution to reduce the number of variables.

2c + c/2 + c + 3b = 7c/2 + 3c/2 = 5c = 180

c = 180/5 = 36 degrees
a = 2c = 72
b = c/2 = 18
d = 3b = 54

They add up to 180, as required.