Final Answer:
Applying the Angle Addition Postulate Warm-Up If m∠BGF = 152°, then m∠AGF = 28°. So, Option A is correct.
Step-by-step explanation:
The Angle Addition Postulate states that the angle formed by two adjacent angles can be found by adding their measures. In this case, we have m∠BGF = 152°. According to the Angle Addition Postulate, m∠BGF + m∠AGF = m∠AGF. Substituting the given measure, we get:
m∠BGF + m∠AGF = 152° + m∠AGF
Now, we know that the sum of angles in a straight line is 180°. So, m∠BGF + m∠AGF = 180°. Substituting this into the equation:
180° = 152° + m∠AGF
Solving for m∠AGF:
m∠AGF = 180° - 152°
m∠AGF = 28°
Therefore, the final answer is m∠AGF = 28°, which corresponds to Option A.
In summary, by applying the Angle Addition Postulate and recognizing the straight line angle relationship, we determined that the measure of ∠AGF is 28°. This process involves setting up an equation based on the postulate, using the known angle measure, and solving for the unknown angle. The solution, 28°, aligns with Option A as the correct answer.