Answer:

120°, 130°, 150°, 9.6°, 6.4°

Step-by-step explanation:

We know that the sum of the interior angles of a pentagon is (5-2) × 180° = 540°.

We can start by finding the measure of the two unknown angles using the ratio given. Let the measures of the two unknown angles be 12x and 8x, where x is a constant. Then we have:

12x + 8x = 20x (the sum of the two unknown angles)

20x + 120° + 130° + 150° = 540° (the sum of all five angles)

300x = 240°

x = 0.8°

Therefore, the measures of the two unknown angles are:

12x = 9.6°

8x = 6.4°

So the measures of the five interior angles of the pentagon are:

120°, 130°, 150°, 9.6°, 6.4°.