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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