1. **State the problem:** We have a kite-shaped quadrilateral ABCD with given angles $\angle A = 76^\circ$ and $\angle C = 100^\circ$. We need to find the measure of $\angle B$. 2. **Recall kite properties:** In a kite, two pairs of adjacent sides are equal: $AB = AD$ and $BC = CD$. Also, the kite is a convex quadrilateral, so the sum of all interior angles is $360^\circ$. 3. **Use the angle sum formula:** The sum of interior angles in any quadrilateral is 360 degrees. So, $$\angle A + \angle B + \angle C + \angle D = 360^\circ$$ 4. **Substitute known values:** $$76^\circ + \angle B + 100^\circ + \angle D = 360^\circ$$ 5. **Simplify:** $$\angle B + \angle D = 360^\circ - 176^\circ = 184^\circ$$ 6. **Use kite angle property:** In a kite, the angles between unequal sides are equal. Since $AB = AD$ and $BC = CD$, angles $B$ and $D$ are equal. So, $$\angle B = \angle D$$ 7. **Set up equation:** $$\angle B + \angle B = 184^\circ$$ $$2 \angle B = 184^\circ$$ 8. **Solve for $\angle B$:** $$\angle B = \frac{184^\circ}{2} = 92^\circ$$ **Final answer:** $$\boxed{92^\circ}$$