Determine if the statement is always, sometimes or never true. there are 250 degrees in the sum of the interior angles of a polygon.
a. always
b. sometimes
c. never

This statement is never true for convex polygons.

1. Consider the smallest polygon - triangle. As known the sum of measures of interior angles of  triangle is 180° (not 250°).

2. The next are quadrilaterals. If you connect two opposite vertices of any quadrilateral, then you get diagonal, which divides the quarilateral into two triangles and the sum of the measures of interior angles of an arbitrary quadrilateral is the sum of the measures of interior angles of these two triangles: 180°+180°=360° (>250°).

3. If you consider pentgons, hexagons and so on, you can noticed then each of these n-sided polygons can be formed by adding triangle to the corresponding (n-1)-sided polygon, then the sum of the measures of interior angles of n-sided polygon is the sum of the measures of interior angles of (n-1)-sided polygon plus 180° (will be greater than 360°). This means that with increasing number of sides, the sum of the measures of the interior angles of a polygon also increases and can never be equal to 250°.

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.