Tangent Angle 386277

1. **Problem Statement:** We are given a circle with a tangent line $EDC$ touching the circle at point $D$. We know the angle between the tangent $DC$ and chord $DB$ is $29^\circ$. We need to find the size of angle $\theta$ at point $B$, which is the angle between $BA$ and $BD$. 2. **Key Theorem:** The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment of the circle. This is known as the Alternate Segment Theorem. 3. **Applying the Theorem:** Since $EDC$ is tangent at $D$ and $DB$ is a chord, the angle between tangent $DC$ and chord $DB$ is $29^\circ$. By the Alternate Segment Theorem, this angle equals the angle subtended by chord $DB$ in the alternate segment, which is angle $\theta$ at point $B$. 4. **Conclusion:** Therefore, the size of angle $\theta$ is equal to $29^\circ$. 5. **Reason:** The Alternate Segment Theorem states that the angle between a tangent and a chord at the point of contact equals the angle in the alternate segment of the circle. **Final answer:** $$\theta = 29^\circ$$