Question

find x, and then any unknown angles in the quadrilateral. this figure is not drawn to scale

Explanation:

Step1: Use the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \(360^{\circ}\). So, \((x + 26)+x+(3x - 13)+(3x - 13)=360\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+x + 3x+3x)+(26-13 - 13)=360\), which simplifies to \(8x=360\).

Step3: Solve for \(x\)

Divide both sides of the equation \(8x = 360\) by \(8\), so \(x=\frac{360}{8}=45\).

Step4: Find the angles

• Angle \(P=(x + 26)^{\circ}\). Substitute \(x = 45\), then \(P=(45 + 26)^{\circ}=71^{\circ}\).
• Angle \(R=x^{\circ}=45^{\circ}\).
• Angle \(T=(3x - 13)^{\circ}\). Substitute \(x = 45\), then \(T=(3\times45-13)^{\circ}=(135 - 13)^{\circ}=122^{\circ}\).
• Angle \(S=(3x - 13)^{\circ}\). Substitute \(x = 45\), then \(S=(3\times45-13)^{\circ}=122^{\circ}\).

Answer:

\(x = 45\), \(\angle P=71^{\circ}\), \(\angle R = 45^{\circ}\), \(\angle T=122^{\circ}\), \(\angle S=122^{\circ}\)