Question

Use the diagram and equations below to match the following angles with their correct measures. Given Z = 2b + 6 and Y = 3b - 1. 1. W 130° 2. X 140° 3. Y 40° 4. Z 50°

Answer 1

a) ∠Z=40°

b) ∠Y=50°

c) ∠W=130°

d) ∠X=140°

Explanation:

Answer 2

the picture in the attached figure

we know that
∠Y+∠Z=90°
∠Z=2b+6 ∠Y=3b-1
so
(2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°
∠Z=2b+6---- 2*17+6-----> ∠Z=40°
∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles
so
∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles
so
∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

the answers are
a) ∠Z=40°
b) ∠Y=50°
c) ∠W=130°
d) ∠X=140°