Find the measure of x. line pu has points r and s between points p and u, lines qr and st are parallel, line qr intersects line pu at point r, line st intersects line pu at point s, the measure of angle prq is 135 degrees, and the measure of angle ust is 15 ( x plus 2 ) degrees. x = −1 x = 7 x = 9 x = 13

The value of x is 1

Step-by-step explanation:

* Lets explain how to solve the problem

- Line PU has points R and S between points P and U

- Line QR intersects line PU at point R

- Line ST intersects line PU at point S

- Lines QR and ST are parallel

- Look to the attached figure

∵ QR // ST

∴ m∠TSU = m∠QRU ⇒ corresponding angles

∵ m∠TSU = 15(x + 2)°

∴ m∠QRU = 15(x + 2)

∵ Points P, R, S lie on the same line

∵ RQ intersects PS at R

∵ m∠PRQ + m∠QRU = 180° ⇒ straight angle

∵ m∠PRQ = 135°

∵ m∠QRU = 15(x + 2)°

∴ 135 + 15(x + 2) = 180

∴ 135 + 15x + 30 = 180

- Add like terms

∴ 15x + 165 = 180

- Subtract 165 from both sides

∴ 15x = 15

- Divide both sides by 15

∴ x = 1

∴ The value of x is 1

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18. g

20. h 30 degree turn.

21. d 90 degree angles

and also 19 is a. a sphere not a cirlcle

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the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.