Question

TIMED

Find the value of x and the value of y.

A.
x = 10, y = 130
B.
x = 65, y = 10
C.
x = 65, y = 130
D.
x = 130, y = 10

Answer 1

see the attached figure to better understand the problem

we know that
∡ABC=90-60-----> 30°
∡ACB=90-40-----> 50°
∡BAC+∡ABC+∡ACB=180°
so
∡BAC=180-(∡ABC+∡ACB)------> 180-(30+50)----->∡BAC= 100°

∡BAC+∡DAC=180--------> supplementary angles
∡DAC=180-∡BAC-----> 180-100------> ∡DAC=80°

(2x+y)=∡FAD+∡DAC
∡FAD=∡GBA-------------> corresponding angles
∡FAD=60°
(2x+y)=60+80------> 2x+y=140--------> equation 1

∡BAJ=90-60------> ∡BAJ=30°
(2x-y)=∡FAJ+∡BAJ------> 90+30--------> (2x-y)=120------> equation 2

using a graph tool
see the attached figure

the solution of the system of equations is
x=65°
y=10°

the answer is
x=65°
y=10°