In ΔXYZ, I is the incentre of the ΔXYZ. If ∠XYZ = 40 degree, then what is the value of ∠XIZ ?

110 degree

In \(\Delta \)XYZ, I is the incentre

\(\angle\)XIZ = 90 + (\(\frac{1}{2}\) x  \(\angle\)XYZ)

= \(\angle\)XIZ = 90 + (\(\frac{1}{2}\) x  40)

= \(\angle\)XIZ = 90 + 20

= \(\angle\)XIZ = 110

Therefore, \(\angle\)XIZ is \({110}^\circ\).