Question

Can somebody tell me what I did wrong

Answer 1

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! :)