9514 1404 393
Answer:
- ∠W = 130
- ∠X = 140
- ∠Y = 50
- ∠Z = 40
Step-by-step explanation:
Using 'y' and 'z' to represent angles with the corresponding names, we have ...
y + z = 90
(3b -1) +(2b +6) = 90 . . . . substitute the given expressions
5b +5 = 90 . . . . . . . . . . . . simplify
b +1 = 18 . . . . . . . . . divide by 5
b = 17 . . . . . . . . subtract 1
Then the angles are ...
y = 3b -1 = 3(17) -1 = 51 -1 = 50
z = 2b +6 = 2(17) +6 = 34 +6 = 40 . . . . note that these are complementary, as theys should be
Angles W and Y form a linear pair, so are supplementary:
W = 180 -Y = 180 -50 = 130
Angles X and Z form a linear pair, so are supplementary:
X = 180 -Z = 180 -40 = 140
Then the angle measures are ...
- ∠W = 130
- ∠X = 140
- ∠Y = 50
- ∠Z = 40
