Question

find the value of x.
171°
p
u
t
(x + 3)°
(3x)°
q
r
s
x =

Explanation:

Step1: Use the property of supplementary angles

Since \( \angle PUT\) and \(171^{\circ}\) are supplementary (they form a linear - pair), \( \angle PUT=180^{\circ}-171^{\circ} = 9^{\circ}\).

Step2: Use the angle - sum property

The sum of angles around a point on a straight line (for the non - overlapping angles \( \angle PUT\), \( \angle TUS\), and \( \angle SUR\)) is \(180^{\circ}\). But since \(PT\parallel QR\) (assumed parallel from the arrow - head markings), we can use the property that the sum of the angles \( \angle PUT+(x + 3)+3x=180^{\circ}\). Substitute \( \angle PUT = 9^{\circ}\) into the equation: \(9+(x + 3)+3x=180\).

Step3: Simplify the equation

Combine like terms: \(9+x+3 + 3x=180\), which becomes \(4x+12 = 180\).

Step4: Solve for \(x\)

Subtract 12 from both sides: \(4x=180 - 12\), so \(4x=168\). Then divide both sides by 4: \(x=\frac{168}{4}\).

Answer:

\(x = 42\)