The measure of the angles of a pentagon are in the ratio of 3:3:3:4:5. What is the number of degrees in the measure of the largest angle?
Since the measures of the angles are in the ratio $3:3:3:4:5$, their measures are $3x, 3x, 3x, 4x$, and $5x$ for some value of $x$. The sum of the angle measures in a pentagon is $180(5-2) = 540$ degrees, so we must have  \[3x+3x+3x+4x+5x = 540^\circ.\] Simplifying the left side gives $18x = 540^\circ$, so $x = 30^\circ$, and the measure of the largest angle is $5x = 5(30^\circ) = \boxed{150^\circ}$.
150
Level 3
Prealgebra
Problem: The measure of the angles of a pentagon are in the ratio of 3:3:3:4:5. What is the number of degrees in the measure of the largest angle?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the measure of the angles in the pentagon, first, recognize that the sum of the interior angles of a pentagon is calculated using the formula (n-2) * 180, where n is the number of sides. For a pentagon, n = 5, so the sum is (5-2) * 180 = 3 * 180 = 540 degrees.

Next, denote the angles of the pentagon as 3x, 3x, 3x, 4x, and 5x based on the given ratio of 3:3:3:4:5. The total of these angles can be expressed as:

3x + 3x + 3x + 4x + 5x = 18x.

Set this equal to the total sum of the angles in the pentagon:

18x = 540.

To find x, divide both sides by 18:

x = 540 / 18 = 30.

Now, substitute x back into the expressions for the angles:

The angles are:
3x = 3(30) = 90 degrees,
3x = 90 degrees,
3x = 90 degrees,
4x = 4(30) = 120 degrees,
5x = 5(30) = 150 degrees.

Identify the largest angle among these calculated measures. The angles are 90, 90, 90, 120, and 150 degrees. The largest angle is clearly 150 degrees.

Thus, the final answer is 150.<|END_OF_LATENT|> The final answer is $150$.