Angle Problems?

Question

Help how would you solve this! I dont know where to start.

angle 1 and angle 2 from a linear pair. angle 2 is a supplement of angle 3. angle 4 is a compliment of angle 3.

measure of angle 1 = 5x-1
measure of angle 2 = 2x^2-3x+1
measure of angle 3 = x^2-3x-10
measure of angle 4 =4x +10

Find the measures of the 4 angles.

Answer 1

For starters, a linear pair of angles is the same thing as a pair of supplemental angles. Both mean that the two angles sum to 180 degrees. Complementary (note spelling) angles sum to 90. So you have a1 + a2 = 180, a2 + a3 = 180, and a3 + a4 = 90. You can write that as

5x - 1 + 2x^2 - 3x + 1 = 180
2x^2 - 3x + 1 + x^2 - 3x - 10 = 180
x^2 - 3x - 10 + 4x + 10 = 90

And simplify as

2x^2 + 2x - 180 = 0
3x^2 - 6x - 189 = 0
x^2 + x - 90 = 0

Divide each equation through by the largest common multiple of its terms (2 and 3 for the first two, respectively) to simplify one more time.

x^2 + x - 90 = 0
x^2 - 2x - 63 = 0
(The last equation is the same as the first.)

Now factor the two equations, getting

(x - 9)(x + 10) = 0
(x + 7)(x - 9) = 0

As you can see, x = 9 is a common solution to both equations. Just calculate the given angle measures using x = 9 to get your final answer.

Answer 2

Angle 2 and 3 are supplementary so they have a sum of 180. To find x, add (2x^2-3x+1) and (x^2-3x-10) set = to 180.

3x^2-6x-9=180. To find x, set this equation = to 0, factor out the 3 to simplify and use the quadratic formula. You will get x = 9 and x=-7. Since you are finding length, the only answer that makes sense is 9. Plug in x to find the measure of each angle.

Answer 3

na not me , i like sticking it from every angle. want to see how ?