l is the incentre of the ΔXYZ. If ∠YlZ = 115 degree, then what is the ∠YXZ ?

50 degree

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

\(\angle\)YIZ = 90 + (\(\frac{1}{2}\) x \(\angle\)YXZ)

= 115 = 90 + (\(\frac{1}{2}\) x \(\angle\)YXZ)

= (\(\frac{1}{2}\) x \(\angle\)YXZ) = 115 - 90

= (\(\frac{1}{2}\) x \(\angle\)YXZ) = 25

= \(\angle\)YXZ = 25 x 2 = \({50}^\circ\).