Please help me The measure of an exterior angle of a triangle is x. The measure of the adjacent interior angle is at least twice x. List three possible solutions for x.

x=60°

x=48°

x=21°

Step-by-step explanation:

Inequalities

The sum of the exterior and the interior angle of a triangle is 180°.

The measure of an exterior angle of a triangle is called x, thus the interior angle is 180-x.

This angle is said to be at least twice x, thus:

180 - x ≥ 2x

Adding x:

180 ≥ 3x

Dividing by 3:

60 ≥ x

Swapping the inequality:

x ≤ 60°

The measure of x must be less or equal to 60°.

Three possible solutions are:

x=60°

x=48°

x=21°

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer