Question

find the measure of angle x in the figure.
note: angles not drawn to scale.
angle x measures □^{circ}

Explanation:

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

The formula for the sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For a heptagon (\(n=7\)), the sum of interior angles is \((7 - 2)\times180^{\circ}=900^{\circ}\).

Step2: Set up an equation to find \(x\)

Let the angles be \(a = 132^{\circ}\), \(b = 124^{\circ}\), \(c = 140^{\circ}\), \(d = 124^{\circ}\), \(e = 118^{\circ}\), \(f = 120^{\circ}\), and \(x\). Then \(a + b + c + d+e + f+x=900^{\circ}\). Substitute the values: \(132 + 124+140 + 124+118+120+x=900\).

Step3: Simplify the left - hand side of the equation

\(132+124 = 256\), \(256+140 = 396\), \(396+124 = 520\), \(520+118 = 638\), \(638+120 = 758\). So the equation becomes \(758+x=900\).

Step4: Solve for \(x\)

Subtract \(758\) from both sides: \(x=900 - 758\).

Answer:

\(142\)