In rhombus PQRS shown below, T lies on PQ such that RT is perpendicular to PQ. Diagonal QS intersects RT at W. If the measure of P =118 then find the measure of TWQ. Show how you found your answer

Answer 1

m<Q will equal 72 because consecutive angles of a parallelogram are supplementary. TWQ is a right triangle and one of the acute angles is 36 because diagonals bisect opposite angles of a rhombus. Thus m<TWQ = 180 - 90 - 36 = 54.