Find the measure in the rhombus

Question

In Rhombus STUD, diagonal SU is drawn. If m<USD = 40, find m<STU.

Answer 1

In a rhombus diagonals bisect each pair of opposite angles so m<TSU = m<USD = 40 so that m<TSD = m<USD + m<TSU = 80.

In a parallelogram consecutive angles are supplementary, m<STU + m<TSD = 180. Since m<TSD = 80, m<STU = 100.