Question

answer
solve for a. figures are not necessarily drawn to scale.
question 2

Explanation:

Step1: Determine similar triangles

Since \(\angle T = \angle T\) (common angle) and \(\angle TVU=\angle TSR = 30^{\circ}\), \(\triangle TVU\sim\triangle TSR\) (by AA - Angle - Angle similarity criterion).

Step2: Use the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal. That is \(\frac{TV}{TS}=\frac{TU}{TR}\).
We know that \(TV = 8\), \(TS=8 + 6=14\), \(TU = 4\) and \(TR=x\).
Substituting the values into the proportion \(\frac{8}{14}=\frac{4}{x}\).

Step3: Cross - multiply to solve for \(x\)

Cross - multiplying gives us \(8x=14\times4\).
So \(8x = 56\).
Dividing both sides by 8: \(x=\frac{56}{8}\).

Answer:

\(x = 7\)