Question

find the value of x. the diagram is not to scale.
90
145
45
35

Explanation:

Step1: Calculate the sum of interior angles

The formula for the sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For a pentagon (\(n=5\)), the sum is \((5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up the equation

We know the angles are \(148^{\circ}\), \(90^{\circ}\) (right - angle), \(112^{\circ}\), \(x^{\circ}\), and \((3x + 10)^{\circ}\). So, \(148+90 + 112+x+(3x + 10)=540\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \((148+90+112 + 10)+(x + 3x)=540\), which gives \(360+4x=540\).

Step4: Solve for \(x\)

Subtract \(360\) from both sides: \(4x=540 - 360\), so \(4x=180\). Then divide both sides by \(4\): \(x=\frac{180}{4}=45\).

Answer:

\(45\)