Question

find the value of x and 3x.
3x=

x=

Explanation:

Step1: Recall the sum of interior angles of a pentagon

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

Step2: Set up the equation

We have the angles \(45^{\circ},45^{\circ},135^{\circ},135^{\circ},x + 3x\). So, \(45+45 + 135+135+x + 3x=540\).
Simplify the left - hand side: \((45 + 45+135 + 135)+4x=540\).
\(360+4x=540\).

Step3: Solve for \(x\)

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

Step4: Find the value of \(3x\)

Since \(x = 45\), then \(3x=3\times45 = 135\).

Answer:

\(3x = 135\), \(x = 45\)