Question

In $\Delta XYZ;XZ=YZ,\angle X=3a+4and\angle Z=2a-4$.
Calculate $Z$

Answer 1

Since, XZ = YZ
$\angle X=\angle Y$ (Isosceles triangle property)
Now, sum of angles of the triangle,
$\angle X+\angle Y+\angle Z=180$
$3a+4+3a+4+2a-4=180$
$8a+4=180$
$a=22$
Thus, $\angle X=3\times 22+4={70}^{\circ }$
$\angle Y=3\times 22+4={70}^{\circ }$
$\angle Z=2\times 22-4={40}^{\circ }$