Angle B Measure 699445

1. **State the problem:** We need to find the measure of angle $B$ in a triangle where the exterior angle at vertex $D$ is $150^\circ$ and the interior angle at vertex $C$ is $40^\circ$. 2. **Recall the exterior angle theorem:** The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Mathematically, if $\angle D$ is the exterior angle, then: $$\angle D = \angle B + \angle C$$ 3. **Substitute the known values:** $$150^\circ = \angle B + 40^\circ$$ 4. **Solve for $\angle B$:** $$\angle B = 150^\circ - 40^\circ$$ 5. **Calculate:** $$\angle B = 110^\circ$$ 6. **Conclusion:** The measure of angle $B$ is $110^\circ$.