Find the value of x. The diagram is not to scale. Given:
RS=~ST,m<RST=7x-54,m<STU=8x
Since RS is congruent to ST, the angles opposite to these sides, angle RST and angle STU, are also congruent. Therefore, we can set up the following equation:
7x - 54 = 8x
To solve for x, we can subtract 7x from both sides:
-54 = x
Therefore, the value of x is -54.