Question

Find the value of x and y

Answer 1

Answer: x= 15 and y= 12

Explanation:

In the given figure , we have three lines parallel to each other .

We know that when two parallel lines are intersected by a transversal , then the alternate interior angles are congruent.

Also, congruent angles have equal measures.

So , Pair of alternate interior angles have equal measure.

From the given figure ,

62° and (4x+2)° are the pair of alternate interior angles.

Then ,
`4x+2=62`

`\\\Rightarrow\ 4x=62-2=60`

`\\\Rightarrow\ x=(60)/(4)=15`

Also, 6y° and 72° are the pair of alternate interior angles.

`6y=72\\\Rightarrow y=(72)/(6)=12`

Hence, the value of x= 15 and y= 12 .

Answer 2

x=15, y=12

Explanation:

Opposite interior angles have the same measure. Hence ...

... 62° = (4x+2)°

... 60 = 4x . . . . . divide by °, subtract 2

... 15 = x . . . . . . . divide by 4

And ...

6y° = 72°

... y = 12 . . . . . . . divide by 6°