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3 years ago

What is the value of x given that figure PTRA is an isosceles trapezoid ?! Please help !

Mathematics

2 answers:

sammy [17]3 years ago

6 0

Since it is a Trapezoid:

TR is Parallel to PA

For a Parallel lines the sum of the 2 opposite interior angles add up to 180

Therefore:

x + (3x + 16) = 180

x + 3x + 16 = 180

4x + 16 = 180

4x = 180 - 16

4x = 164

x = 164/4

x = 41

x = 41 degrees. Option C.

GrogVix [38]3 years ago

4 0

HOPE it helps!!!!!!!
plz mark as a brainliest answer!!!!!

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Tpy6a [65]

Since segments ST and PQ are parallel, triangles SRT and PRQ are similar due to the AAA postulate. In general, the ratio between the corresponding sides of two similar triangles is constant; therefore,

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Finding PR and RS,

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Then,

$\frac{12}{PR}=\frac{TS}{15}$ $\begin{gathered} \Rightarrow\frac{12}{PR}=\frac{4+PS}{15} \\ \Rightarrow\frac{12}{PS+12}=\frac{4+PS}{15} \end{gathered}$

Solving for PS,

$\begin{gathered} 12\cdot15=(PS+12)(PS+4) \\ \Rightarrow180=PS^2+16PS+48 \end{gathered}$

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$\begin{gathered} \Rightarrow PS^2+16PS-132=0 \\ \Rightarrow PS=\frac{-16\pm\sqrt[]{16^2-4(-132)}}{2}=\frac{-16\pm28}{2} \\ \Rightarrow PS=-22,6 \end{gathered}$

And PS is a segment; therefore, it has to be positive.

Hence, the answer is PS=6

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