In the figure below, lines
←→
R
V
and
←→
Q
U
are perpendicular and intersect at point Z.
A line W-S passes through the point Z. Rays Z-S and Z-T forms an angle X degree. The rays Z-T and Z-U forms an angle X plus 15 degrees. The rays Z-W and Z-V forms an angle X plus 30 degrees.
What is the degree measure of
∠
R
Z
S
?
A.
15°
B.
30°
C.
45°
D.
60°
B. 30°
Since lines R-V and Q-U are perpendicular, we have right angles at Z.
Angle RZS = X.
Angle ZSU = X + 15.
Angle ZVW = X + 30.
As the sum of the angles around point Z is equal to 360 degrees, we have:
X + X + 15 + X + 30 = 360
3X + 45 = 360
3X = 315
X = 105
So, angle RZS = 105 degrees.
Therefore, the degree measure of angle RZS is 30 degrees.