Question

given the image, choose the correct reason for each statement of the proof. 3. statement 2: $x+(3x + 20)=180$ a. substitution property b. angle addition postulate c. division property of equality d. simplify e. subtraction property of equality

Explanation:

The Angle Addition Postulate states that if two angles are adjacent (share a common side and vertex), then the sum of their measures is equal to the measure of the larger angle they form together. In the given image, the two angles \(x^{\circ}\) and \((3x + 20)^{\circ}\) are adjacent and form a linear pair (a straight - line angle, which measures \(180^{\circ}\)). So, we use the Angle Addition Postulate to write the equation \(x+(3x + 20)=180\).

Answer:

B. Angle Addition Postulate