Final answer:
Noah needs 540 bricks for the arch.
Step-by-step explanation:
Let's start by finding the number of bricks that Noah sets aside for broken ones. He sets aside 15 bricks. Therefore, he has 150 - 15 = 135 bricks left to use.
Next, we need to find the number of bricks needed for the arch. The arch takes 4 times as many bricks as the chimney, which means it requires 4 * 135 = 540 bricks.
Therefore, Noah needs 540 bricks for the arch.