the measure of an angle is 12 less than twice the measure of its supplement. what is the measure of the angle?

116°

Step-by-step explanation:

So we don't know what the angle and we will name it angle x . We also know that angle x  is  12 less than the measure of its supplement and we will represent  its supplement by y. Now using the given information we can represent x by the equation x = 2y - 12    

Supplementary angles add up to 180 degrees. So we know that x  and y has to add up to 180  and x is equal to 2y-12  so we can also represent it by the equation   y + (2y -12) = 180  now solve for y to find the supplement.

y + 2y - 12 = 180

3y - 12 = 180  

     +12      +12

3y = 192

y = 64    

So we know the supplement is 64  and the measure of that angle has to be 12  less than two times the supplement.

so x= 2(64) - 12

  x  = 128 - 12

x = 116  

So the measure of that angle is 116 degrees.

Now add it to its supplement to see if it equals 180 degrees.

116 + 64  = 180

 180 = 180  

So it works!

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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

for any of you who need the translation here it is

step-by-step explanation:

find the angular size of the equatorial radius of the earth, if the horizontal parallax of the sun