Answer:
C) 3.0
Step-by-step explanation:
Right triangles SQT and SQR are congruent by the HL Theorem because the hypotenuse and one leg of ΔSQT is congruent to the hypotenuse and corresponding leg of ΔSQR.
Since corresponding angles in congruent triangles have equal measures, it follows that m∠TSQ ≅ m∠RSQ. Therefore:
[tex]m\angle TSQ=m\angle RSQ\\\\\\(2x+24)^{\circ}=30^{\circ}\\\\\\2x+24=30\\\\\\2x+24-24=30-24\\\\\\2x=6\\\\\\\dfrac{2x}{2}=\dfrac{6}{2}\\\\\\x=3[/tex]
So, the value of x is:
[tex]\huge\boxed{\boxed{3.0}}[/tex]
