Question

In the given figure line PQ and RS are parallel .For what the value of x will the lines AB and CD be parallel

Answer 1

PEF=EFH=2x ..............( Alt . Angles )

EFH=FHD=2x.............(Alt . Interior angle)

SHD+FHD=180

3x-15+2x=180

5x-15=180

5(x-3)=180

x=36°+3°

x=39°

Answer 2

Answer:

$39^{o}$

Step-by-step explanation:

Given: PQ║RS

To find:

The value of x

Solution;

When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines.

Two angles that are created when a line crosses two other lines and they are located on the transverse line's opposite and relative sides. The alternate angles are equal if the two lines that are crossed are parallel.

∠PEF=∠EFH=2x _______(alternate angels)

∠EFH=∠FHD=2x_______(Alternate interior angles)

∠SHD+∠FHD=$180^{o}$

3x-15+2x=$180^{o}$

5x-15=$180^{o}$

5(x-3)=$180^{o}$

$x=36^{o} +3^{o} \\x=39^{o}$

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