Question

$\text{Use the information given in the alongside diagram to find the value of x, y and z.}$

Answer 1

$\text{In the given figure,}\text{ABCD is a parallelogram and AC is its diagonal which bisects the opposite angle}\because \text{Opposite sides of a parallelogram are equal}\therefore 3x+14=2x+25\Rightarrow 3x-2x=25-14\Rightarrow x=11\therefore x=11cm\angle DCA=\angle CAB\left(\text{Alternate angles}\right)\therefore y+9^{\circ }=24=y={24}^{\circ }-9^{\circ }={15}^{\circ }\therefore \angle DAB=3y^{\circ }+5^{\circ }+{24}^{\circ }=3\times 15+5+{24}^{\circ }={50}^{\circ }+{24}^{\circ }={74}^{\circ }\therefore \angle ABC={180}^{\circ }-\angle DAB={180}^{\circ }-{74}^{\circ }={106}^{\circ }\therefore z={106}^{\circ }Hencex=11cm,y={15}^{\circ },z={106}^{\circ }$