The diagonals of parallelogram QRST and intersect at point U. If RS = 10, ST = 12, and RU = 9.5, find the length of

From the given equation we have x=z and t=z. Therefore, option B is the correct answer.

Given that, lines k, l, and m intersect at a point.

What is vertical angle theorem?

Vertical angles theorem or verticallyopposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

From the given figure,

Using vertical angle theorem, we have

x°=t°

y°=u°

w°=z°

If x + y = u + w, then

x+u=u+z

⇒ x=z

If x + y = u + w, then

t+u=u + z

⇒ t=z

So, x=z and t=z

From the given equation we have x=z and t=z. Therefore, option B is the correct answer.

To learn more about the vertical angle theorem visit:

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Answer:

B)

Step-by-step explanation:

First, let's write down what we know based on the Vertical Angle Theorem and the info given by the question:

1. Vertical angle theorem claims that opposite angles are the same, therefore:

• y=u
• x=t
• w=z

2. We know from the problem that:

• x+y = u+w

3. Now for the proofing:

Since  x+y = u+w, let us try to cross off the variable u and see if we can get x equaling to w.

We know that y=u, so let us switch out y for another u, allowing the same variable to cross out

x+y = u+w --> x+u = u+w --> x=w

Ok now we know x=w, and recall that w=z. So x would also equal to z!

Let us try to proof z=t:

We know that x=t

But now we also know that x=z (from previous)

Therefore we can substitute the z in for x in x=t and voila z=t!

Try finding out if y=w. No matter how many equations you create, they are not the same. It would not make sense either if you use this equation: x+y = u+w. If w and x are the same then y cannot be anything except being equal to "u". We cannot prove that u is equal to anything else either.

Therefore the answer is B)

First page:

Angles B and C >>> vertical angles

C + D is 180 because they form a >>> straight line

D and E are congruent bc they are alternating interior.

Second page:

If A = 72 degrees, then D is 72 degrees. E and G would also be 72 degrees.

If A = 72, just remember that A + B = 180 (bc together they are a straight line), so 180-72 = 108. So Angle B is 108 degrees.

If B is 108 degrees, then C, F and H are also 108 degrees.

So the actual questions in the order listed:

B = 108 degrees

D = 72 degrees

E = 72 degrees

F = 108 degrees

H = 108 degrees

G = 72 degrees

Answer:

997/2

Step-by-step explanation: