Question

Help me with those two questions

Answer 1

Given:

A figure in which a transversal line intersect two parallel lines.

$m\angle 2=4x+7, m\angle 7=5x-13, m\angle 5=68$ and $m\angle 3=3y-2$.

To find:

The value of x and y.

Solution:

We know that, if a transversal line intersect two parallel lines, then

(1) Alternate exterior angles are equal.

(2) Same sided interior angles are supplementary. So their sum is 180 degrees.

In the given figure j and k are parallel lines and l is a transversal line.

From the given figure, it is clear that,

$m\angle 2=m\angle 7$                (Alternate exterior angles are equal)    

$4x+7=5x-13$

$7+13=5x-4x$

$20=x$

Therefore, the value of x is 20.

Now,

$\angle 3+\angle 5=180$     (Same sided interior angles are supplementary)

$3y-2+68=180$

$3y+66=180$

$3y=180-66$

$y=\dfrac{180-66}{3}$

$y=\dfrac{114}{3}$

$y=38$

Therefore, the value of y is 38.