Question

1.) What is m∠PTS? 2.) What is the value of x?

Answer 1

Observe the figure below.

When two lines intersect each other, vertically opposite angles are always equal.

So, $m \angle PTS = m \angle RTQ$

$[11(y-10)]^\circ = (4y-5)^\circ$

$[11y-110]^\circ = (4y-5)^\circ$

$[11y-4y]^\circ = (110-5)^\circ$

$7y^\circ = 105^\circ$

$y = 15^\circ$

So, the measure of 'y' is 15 degrees.

The measure of angle PTS = 11(y-10)

= 11(15-10)

= 55 degrees

So, the measure of angle PTS is 55 degrees.

Answer 2

STR and QTP are both equal 180
so PTS +PTR=180 andQTR+PTR=180 which means
PTS=QTR(for a shorter explanation they are staying against each other in a line cross

11y-110=4y-5
7y=105
y=105:7
y=15 grafe which means
PTS
y*4-5=55 grade