Question

given: segmet RS is congruent to segment ST, angle RST = 7x - 54, angle STU = 8x

Find the value of X

Answer 1

Is there a diagram that goes with the question? If so, you can use the Draw button under the reply box.

Answer 2

yea there is sorry

Answer 3

sorry the t and the u is suppose to be on the right side

Answer 4

Does it look like this?

Answer 5

7x-54

Answer 6

yea

Answer 7

If angle STU = 8x, can you tell me what is angle STR?

Answer 8

is it 7x sorry im not good at geometry

Answer 9

Okay. STR and STU are called linear pair of angles. Together they form a straight line and so the sum of the angles will be 180 degrees. So if STU = 8x, STR will be (180 - 8x).

The problem states that segment RS = ST. That means, angle SRT = angle STR
So angle SRT = angle STR = (180 - 8x).

The three angles of a triangle add to 180. So angle RST + angle SRT + angle STR = 180

Substitute: 7x - 54 + 180 - 8x + 180 - 8x = 180

Can you simplify and solve for x from here?

Answer 10

yea

Answer 11

cool.

Answer 12

thank you !

Answer 13

you are welcome.