If angle $CBD$ has a measure of $140°$, what is the measure of angle $ABD$ if point $A$ lies on the terminal side of angle $CBD$ such that $A$, $B$, and $D$ are collinear and $B$ is the vertex?

• A. $60°$
• B. $50°$
• C. $40°$
• D. $70°$

Answer: (D)

Verified step by step guidance

1. Identify the given angle \( \angle CBD = 140^\circ \) and note that points \( A \), \( B \), and \( D \) are collinear with \( B \) as the vertex.
2. Since \( A \), \( B \), and \( D \) are collinear, the angle formed by \( A \), \( B \), and \( D \) is a straight angle, which measures \( 180^\circ \).
3. Recognize that \( \angle CBD \) and \( \angle ABD \) share the vertex \( B \) and lie on opposite sides of the line through \( A \), \( B \), and \( D \), making them supplementary angles.
4. Use the supplementary angle relationship: \( \angle ABD + \angle CBD = 180^\circ \).
5. Solve for \( \angle ABD \) by subtracting the measure of \( \angle CBD \) from \( 180^\circ \): \( \angle ABD = 180^\circ - 140^\circ \).