Which statement reflects the Angle Addition Postulate?

Which statement reflects the Angle Addition Postulate?

• A. The whole angle is the difference of its parts.
• B. m∠ABC + m∠CBD = m∠ABD.
• C. The sum of angle measures equals twice a part.
• D. The sum of the parts equals the product of the whole.

Answer: (B)

The Angle Addition Postulate says that when a ray lies inside an angle, it splits the angle into two smaller adjacent angles whose measures add up to the measure of the whole angle. Here, ray BC sits inside angle ABD, creating two smaller angles: ABC and CBD. Therefore the measure of the whole angle ABD is the sum of the two parts: m∠ABD = m∠ABC + m∠CBD, which is the same as m∠ABC + m∠CBD = m∠ABD. This is exactly the relationship described by the postulate. (For example, if m∠ABC = 25 and m∠CBD = 35, then m∠ABD = 60.) Other formulations like the whole being a difference, or involving a product or a twice-part sum, don’t describe how a single angle is split into two parts.

The Angle Addition Postulate says that when a ray lies inside an angle, it splits the angle into two smaller adjacent angles whose measures add up to the measure of the whole angle. Here, ray BC sits inside angle ABD, creating two smaller angles: ABC and CBD. Therefore the measure of the whole angle ABD is the sum of the two parts: m∠ABD = m∠ABC + m∠CBD, which is the same as m∠ABC + m∠CBD = m∠ABD. This is exactly the relationship described by the postulate. (For example, if m∠ABC = 25 and m∠CBD = 35, then m∠ABD = 60.) Other formulations like the whole being a difference, or involving a product or a twice-part sum, don’t describe how a single angle is split into two parts.