Question

solve for x.
options:
a. 10
b. 12
c. 3
d. 8

Explanation:

Step1: Use triangle - similarity property

Since the two triangles are similar (by the AA - similarity criterion as the angles are equal because of the parallel - like structure indicated by the equal - side markings), the ratios of their corresponding sides are equal. The ratio of the sides gives the equation: $\frac{2x}{- 10 + 2x}=2$.

Step2: Cross - multiply

Cross - multiplying the equation $\frac{2x}{-10 + 2x}=2$ gives $2x=2(-10 + 2x)$.

Step3: Expand the right - hand side

Expanding $2(-10 + 2x)$ gives $2x=-20 + 4x$.

Step4: Solve for x

Subtract $2x$ from both sides: $0=-20 + 4x-2x$. Then $2x = 20$, and $x = 10$.

Answer:

A. 10