Question

find giving reasons the measure of angle ABCD

Answer 1

First of all, a = 65 because its vertically opposite angle is 65.

Now, look at the two vertical parallel lines and their transversal. a and b are alternate angles.

So, b = 65.

Now, look at the two horizontal parallel lines and their transversal. b and c are alternate angles.

So, c = 65.

Now, c and d form a linear pair.

c + d = 180
∴65 + d = 180
∴ d = 180 - 65
∴ d = 115

Now, again look at the two parallel horizontal lines and their transversal.
d and e  are alternate angles.

So, e = 115

Thus,
a = b = c = 65 
and d = e = 115

Answer 2

Answer:

Step-by-step explanation:

First of all, a = 65 because its vertically opposite angle is 65.

Now, look at the two vertical parallel lines and their transversal. a and b are alternate angles.

So, b = 65.

Now, look at the two horizontal parallel lines and their transversal. b and c are alternate angles.

So, c = 65.

Now, c and d form a linear pair.

c + d = 180

∴65 + d = 180

∴ d = 180 - 65

∴ d = 115

Now, again look at the two parallel horizontal lines and their transversal.

d and e  are alternate angles.

So, e = 115

Thus,

a = b = c = 65  

and d = e = 115