Question

In the figure the arrow head segments are parallel then find the value of x and y.

Answer 1

y=180-(105+35)
=180-140
=40
x=y
=40

Answer 2

Answer:

x=40° and y=40°

Step-by-step explanation:

∠FCG=∠BCE=105°( vertically opposite angles)

Now, using the straight angle property, ∠BCA+∠BCE+∠ECD=180°

⇒35°+105°+y=180°

⇒y=40°

Also, ∠BCD=∠BCE+∠ECD

                   = 105°+40°

       ∠BCD  = 145°

Now, ∠BCA+∠ACF+∠FCG=180°

⇒35°+∠ACF+105°=180°

⇒∠ACF=40°

Therefore, ∠BCF=75°

Now, ∠1=∠BCF=75°(Alternate angles)

Also, ∠1+∠ABC=180°(Straight angle property)

∠ABC=180-75

∠ABC=105°

Now, using Angle sum property in triangle ABC,

∠BAC+∠ABC+∠BCA=180°

x+105°+35°=180°

x=40°