Question

find the measure of \\( \angle ost \\).
\\( m \angle ost = \square ^ { \circ } \\)

Explanation:

Step1: Use the property of consecutive interior angles

Since \(OP\parallel QR\), \(\angle OST\) and \(\angle QTS\) are consecutive interior angles. So \((10x + 43)+(15x + 12)=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(10x+15x+43 + 12=180\), \(25x+55 = 180\).
Subtract 55 from both sides: \(25x=180 - 55\), \(25x=125\).
Divide both sides by 25: \(x = 5\).

Step3: Calculate \(\angle OST\)

Substitute \(x = 5\) into \(10x+43\).
\(10x+43=10\times5 + 43=50+43=93\).

Answer:

\(93\)