1. the sum of the interior angle measures of a convex dodecagon.

2. the measure of each interior angle of a regular 20-gon

dodecagon --- 12 sides

It must be regualar, that is, all sides must be equal and all 12 interior angles are equal.

sum = 180(n-2)
so each angle = 180(n-2)/n

for 12 sides:
each angle = 180(12-2)/12 = 150°

you do the one with 20sides

162

correct

To find the sum of the interior angle measures of a convex dodecagon:

Step 1: Recall that a dodecagon is a polygon with 12 sides.

Step 2: Use the formula for finding the sum of the interior angles of a polygon, which is (n - 2) * 180, where n represents the number of sides of the polygon.

Step 3: Substitute the value of n with 12: (12 - 2) * 180 = 10 * 180 = 1800.

Therefore, the sum of the interior angle measures of a convex dodecagon is 1800 degrees.

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To find the measure of each interior angle of a regular 20-gon:

Step 1: Recall that a regular polygon has equal side lengths and equal interior angles.

Step 2: Use the formula for finding the measure of each interior angle in a regular polygon, which is (n - 2) * 180 / n, where n represents the number of sides of the polygon.

Step 3: Substitute the value of n with 20: (20 - 2) * 180 / 20 = 18 * 180 / 20 = 162 * 9 = 1458 degrees.

Therefore, the measure of each interior angle of a regular 20-gon is 1458 degrees.