Find the value of x. The diagram is not to scale. Given RS=ST, m April 5, 2022September 21, 2021 by thanh

3 Answers

• We know from basic geometry that

  <SRT + <RST = <STU. We also know that

  <SRT = <STR = 180 – 7x. So we have

  180 – 7x + 5x – 24 = 7x, or

  156 = 9x, so x = 52/3 or 17 1/3.

  Answer: none of the above

• m<STR + m<STU = 180. We also know that m<STR + m<RST + m<SRT = 180.

  Since this triangle is isosceles, m<STR = m<SRT. [180 – (5x – 24)]/2 = m<STR.

  7x + [180 -(5x – 24)]/2 = 180

  7x + [180 – 5x + 24]/2 = 180

  7x + 90 -5x/2 + 12 = 180

  9x/2 = 78

  9x = 156

  x = 52/3

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