Help on Q from GMATprep

[Riggz]

I just cant seem to understand how the answer is what it is...pls help thanks!

[rey.fernandez]

(1) is not enough: we know nothing about point U's position, which would determine the measure of x.

(2) is not enough for similar reasons: we know nothing about point Q's position.

(1 & 2)
let's call r the measure of angle R and t the measure of angle T. From the statements we can infer that triangles QRS and STU are isosceles.

Therefore, angle RSQ equals (180-r)/2 and angle UST equals (180-t)/2.

angle RSQ + x + angle UST = 180
(180-r)/2 + x + (180-t)/2 = 180
180 - r + 2x + 180 - t = 360
2x = r + t

Now, because triangle RPT is a right triangle, we know that r + t = 90. Therefore,

2x = 90
x =45

The answer is C.

[Riggz]

thank you! very good explanation!

trick here was to use the isosceles triangle formula!