Answer:
∠ PTS = 55°
Explanation:
∠ PTSand ∠ QTR are vertically opposite angles and are congruent , then
∠ PTS = ∠ QTR ( substitute values )
11(y - 10) = 4y - 5 ← distribute parenthesis on left side
11y - 110 = 4y - 5 ( subtract 4y from both sides )
11y - 4y - 110 = 4y - 4y - 5 ( simplify both sides )
7y - 110 = - 5 ( add 110 to both sides )
7y - 110 + 110 = - 5 + 110 ( simplify both sides )
7y = 105 ( divide both sides by 7 )
y =
, that is
y = 15
Then
∠ PTS = 11(y - 10) = 11(15 - 10) = 11 × 5 = 55°