The sum of the angle measures of any triangle is 180 degrees. Angle #2 is twice the length of Angle #1 and Angle #3 is 15 degrees less than the Angle #2. What is the measure of each angle?

The measure of angle 1 is 39 degrees,the measure of angle 2 is 78 degrees and the measure of angle 3 is 63 degrees.

Step-by-step explanation:

We will represent the measure of angle 1 by x because it is unknown.

It says that the measure of angle 2 is twice angle 1   so we could represent that as  2x  and the measure of angle 2  is 15 less than angle 3 and we could also represent that by  2x - 15.

Now we know they all add up to 180 so add them up and set them equal to 180 and solve for x.

x + 2x + 2x -15 = 180  

5x - 15 = 180

      +15   +15

5x = 195

x = 39  

If x is equal to 39 then the measure of angle 1 is 39 degrees and the measure of angle 2 is twice that so 2(39) = 78   which also gives us the measure of angle 2 as 78.

For angle 3 it says that it has to be 15 less than the measure of angle so  subtract 15 from  78 to find the measure of angle 3.

78 - 15 = 63   The measure angle 3 is 63 degrees. Now add the measures all together to see if they equal 180 degrees .

Check:

39 + 78 + 63 = 180

  180 = 180

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2