Because ∠PTS and ∠QTR are vertical angles, we can use the Vertical Angle Theorem to say they are equal. Therefore:
11(y - 10) = (4y - 5)
Now, solve for y:
11y - 110 = 4y - 5
7y = 105
y = 15
You got up to here, but rather than finding the angle measure they asked for, you put the value of y. So, lets do that. Plug y back into ∠PTS:
11(y - 10)
=11(15 - 10)
=11(5)
=55
Therefore, the measurement of ∠PTS is 55°.
Hope this helps! :)
