Question

In the following figure,find the value of y :-​

Answer 1

Answer:

55 + 25 + x = 180 ----------------→ ( i )

and

55 + 25 + x + y + angle DOF + angle DOE  [considering the center point to be O ]

according to the figure.

looking at the lines EC and DB

The intersect forming vertically opposite angles.

∴ angle DOE = 25

And from eq. ( i ) :

55 + 25 + x = 180

x = 180 - 55 - 25

x = 180 - 80

x = 100

According to the vertically opposite angles property.

if BD and EC intersect at one point and :

angle DOE = 25

then:

angle EOB = angle DOC----------------→ ( ii )

Now plug in the values in eq. ( ii )

∴ 55 + x = angle DOF + y

[put in the x value]

55 + 100 = m + y         [taking angle DOF as m]

155 = m + y

so we can take y = 155 - m

since angle EOD = 25 :

180 - 155 = 25

y = 155 - m