Question

find the value of x.
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x =

Explanation:

Step1: Use vertical angles and angle sum property

Vertical angles are equal. Also, the sum of angles around a point is \(360^{\circ}\). But since \(TP\parallel RQ\), we can use the property that \(\angle SUT+\angle TUR + \angle RUQ+\angle QUP = 180^{\circ}\) (linear - pair related angles). \(\angle TUR=(x + 3)^{\circ}\), \(\angle RUQ=(3x)^{\circ}\), and \(\angle QUP = 171^{\circ}\). But \(\angle SUT\) and \(\angle QUP\) are vertical angles. Wait, no, correct approach: \((x + 3)+3x+171=180\) (since they form a linear - pair).

Step2: Solve the equation

Combine like terms: \(x+3 + 3x+171=180\).
\(4x+174 = 180\).
Subtract 174 from both sides: \(4x=180 - 174\).
\(4x = 6\).
Divide both sides by 4: \(x=\frac{6}{4}=\frac{3}{2}=1.5\).

Answer:

\(1.5\)