9514 1404 393
Answer:
x = 2
Explanation:
Triangles QST and QSR are congruent, so angle QST is congruent to angle QSR.
(3x +24)° = 30°
3x = 6 . . . . . . . . . divide by °, subtract 24
x = 2 . . . . . . . . . . divide by 3
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Additional comment
What matters here is the relationship between the two marked acute angles. The fact that point Q is equidistant from the sides of angle TSR tells you that QS is an angle bisector and the two angles have equal measures. (The definition of an angle bisector is that it is equidistant from the sides of the angle.)
Recognition that the two triangles are congruent is another way to see that the marked acute angles have the same measure. The triangle congruence can be claimed on the basis of the HL theorem, since both are right triangles, have the same hypotenuse (QS), and have legs (QT, QR) with the same measure.