Question

find the value of x in the figure.
(4x - 5)° 117°
(4x - 3)°
(3x - 3)°
118° (3x + 6)°

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 hexagon (\(n = 6\)), the sum is \((6 - 2)\times180^{\circ}=720^{\circ}\).

Step2: Set up the equation

\((4x - 5)+(4x - 3)+118+(3x + 6)+(3x - 3)+117 = 720\)
Combine like terms:
\((4x+4x + 3x+3x)+(-5-3 + 6-3+118+117)=720\)
\(14x+( - 5)+118+117=720\)
\(14x+(113 + 117)=720\)
\(14x+230 = 720\)

Step3: Solve for \(x\)

Subtract \(230\) from both sides:
\(14x=720 - 230\)
\(14x = 490\)
Divide both sides by \(14\):
\(x=\frac{490}{14}=35\)

Answer:

\(x = 35\)