Question

In the figure $\angle X=626\circ \angle XYZ={56}^{\circ }$. If YI and ZI are the bisectors of $\angle XYZ$ and $\angle XZY$ respectively of $\Delta XYZ.$ find $\angle IZY$. in degrees

Answer 1

In $△XYZ$,
$\angle YXZ={62}^{\circ }$
$\angle XYZ={56}^{\circ }$
Sum of angles = 180
$\angle YXZ+\angle ZXYZ+\angle XZY=180$
$62+56+\angle XZY=180$
$\angle XZY={62}^{\circ }$
Since, IZ bisects $\angle XZY$,
$\angle XZI=\angle IZY=\frac{1}{2}\angle XZY=\frac{1}{2}62={31}^{\circ }$
Similarly, IY bisects $\angle XYZ$,
$\angle XYI=\angle IYZ=\frac{1}{2}\angle XYZ=\frac{1}{2}56={28}^{\circ }$
Now, In $△IYZ$,
$\angle IYZ+\angle IZY+\angle YIZ=180$
$31+28+\angle YIZ=180$
$\angle YIZ={121}^{\circ }$