Question

find the value of x. the diagram is not to scale.

90
145
45
35

Explanation:

Step1: Use the formula for the sum of interior angles of a pentagon

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

Step2: Set up the equation

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

Step3: Simplify the left - hand side of the equation

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

Step4: Solve for \(x\)

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

Answer:

\(45\)