Question

1. multiple choice in qrst, $overline{qt}congoverline{ts}$ and $overline{rs}congoverline{ts}$. what is $x$? a 1 b 4 c 12 d 16 e 32 $\frac{1}{2}(14x + 8)$ $6x + 8$

Explanation:

Step1: Set up the equation

Since $\overline{QT}\cong\overline{TS}$ and $\overline{RS}\cong\overline{TS}$, we have $\frac{1}{2}(14x + 8)=6x + 8$.

Step2: Expand the left - hand side

Expand $\frac{1}{2}(14x + 8)$ to get $7x+4$. So the equation becomes $7x + 4=6x + 8$.

Step3: Solve for x

Subtract $6x$ from both sides: $7x-6x+4=6x - 6x+8$, which simplifies to $x+4 = 8$. Then subtract 4 from both sides: $x+4-4=8 - 4$, so $x = 4$.

Answer:

B. 4