Value of x and what are angles m you!

To find the value of x, you want to use the vertical angles theorem.

The vertical angles theorem says that all vertical angles (which is what TRY and QRW are) are congruent to each other. Knowing this you can make an equation where the angles are equal to each other to find the value of x.

TRY = QRW, so:

(x+16) = (4x-5)

1. Add 5 to both sides.

(x+21) = (4x)

2. You can get rid of the parentheses.

x+21 = 4x

3. Subtract x from both sides.

21 = 3x

4. Divide both sides by 3, isolating x.

7 = x

5. Flip this equation around, so:

x = 7

To find the measure of TRY then plug x into the expression for TRY, which is (x+16).

TRY => ((7)+16) = 23

Since TRY is 23, the vertical angles theorem says that QRW is also 23. Add these measures up.

23+23 = 46

A line's measure is 180 degrees, so two lines would add up to 360 degrees. Subtract 46 from 360 to find the remaining degrees.

360-46 = 314

TRQ and YRW must be congruent to each other so that means you can divide 314 by 2.

314/2 = 157

Answers are:

TRY = 23

TRQ = 157

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

25% is the answer