Question

A parallelogram AXZ has two sides 60 m and 25 m and a diagonal 65 m long. Find z.

Answer 1

$Given-ABCDisaparallelogram.\angle A=z,\angle B={100}^O,\angle C=x,\angle D=y.Tofindout-Thevaluesofx,y,z.Solution-ABCDisaparallelogram.\therefore AB\parallel DC\&ADisthetransversal.i.e\angle ABC\&\angle BCDaresamesidedinternalangles.\therefore m\angle ABC+m\angle BCD={180}^o.⟹m\angle BCD={180}^o-{100}^O(m\angle ABC={100}^{O}given).⟹m\angle BCD={80}^o=x.Butx=z\&y={100}^O(oppositeanglesofaparallelogramareequal.)Sox={80}^{O}y={100}^{O}z={80}^O.Ans-x={80}^{O}y={100}^{O}z={80}^O.$