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 interior angles of a quadrilateral is \(360^{\circ}\). So, \((3x - 40)+110 + 90+x=360\).

Step2: Simplify the equation

Combine like - terms: \(3x+x-40 + 110+90 = 360\), which is \(4x+( - 40+110 + 90)=360\), then \(4x + 160=360\).

Step3: Solve for \(x\)

Subtract \(160\) from both sides: \(4x=360 - 160\), so \(4x = 200\). Divide both sides by \(4\): \(x=\frac{200}{4}=50\).

Step4: Find the angle at \(A\)

Substitute \(x = 50\) into \(3x-40\). \(3x-40=3\times50 - 40=150 - 40 = 110^{\circ}\).

Answer:

\(x = 50\), \(\angle A=110^{\circ}\)