Question

please answer this question, anyone who want 20 points​

Answer 1

Given :-

PQ || ST

To Find :-

Angle QRS

By construction :-

Draw a line XY || to both PQ and ST.

______________________________________________

★Let's do it ★

Let Angle PQR = 1

Also,

Angle TSR = 2

Angle QRX = 3

Angle QRS = 4

Angle SRY = 5

Now,

Angle 1 + Angle 3 = 180 degree ( sum of interior angles on same side of transversal is 180 degree )

110 + Angle 3 = 180

Angle 3 = 180 - 110 = 70

$\therefore$ Angle QRX = 70 degree.

Also,

Angle 2 + Angle 5 = 180 degree

130 + Angle 5 = 180

Angle 5 = 180 - 130 = 50

$\therefore$ Angle SRY = 50 degree.

✩Now✩

Angle 3 + Angle 4 + Angle 5 = 180 degree ( sum of angles on straight line is 180 degree )

70 + 50 + Angle 4 = 180

120 + Angle 4 = 180

Angle 4 = 180 - 120 = 60

$\therefore$ Angle QRS = 60 degree.

$\Large\star\underline{\underline{\sf{ \color{lime}{Ans\:Completed} }}}\star$

Answer 2

Given :-

PQ || ST

To Find :-

Angle QRS

By construction :-

Draw a line XY || to both PQ and ST.

______________________________________________

★Let's do it ★

Let Angle PQR = 1

Also,

Angle TSR = 2

Angle QRX = 3

Angle QRS = 4

Angle SRY = 5

Now,

Angle 1 + Angle 3 = 180 degree ( sum of interior angles on same side of transversal is 180 degree )

110 + Angle 3 = 180

Angle 3 = 180 - 110 = 70

$\therefore$ Angle QRX = 70 degree.

Also,

Angle 2 + Angle 5 = 180 degree

130 + Angle 5 = 180

Angle 5 = 180 - 130 = 50

$\therefore$ Angle SRY = 50 degree.

✩Now✩

Angle 3 + Angle 4 + Angle 5 = 180 degree ( sum of angles on straight line is 180 degree )

70 + 50 + Angle 4 = 180

120 + Angle 4 = 180

Angle 4 = 180 - 120 = 60

$\therefore$ Angle QRS = 60 degree.

$\Large\star\underline{\underline{\sf{ \color{lime}{Ans\:Completed} }}}\star$