Question

find ( mangle a ). the diagram is not to scale.
73
63
117
107

Explanation:

Step1: Calculate the sum of interior angles of a pentagon

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: Find the interior angle adjacent to \(\angle A\)

Let the interior angle adjacent to \(\angle A\) be \(x\). Then \(x+\angle A = 180^{\circ}\) (linear - pair of angles).
We know that \(118^{\circ}+104^{\circ}+96^{\circ}+115^{\circ}+x=540^{\circ}\).
First, sum the known angles: \(118 + 104+96 + 115=(118 + 104)+(96 + 115)=222+211 = 433^{\circ}\).
Then, solve for \(x\): \(x=540^{\circ}-433^{\circ}=107^{\circ}\).

Step3: Calculate \(\angle A\)

Since \(x+\angle A=180^{\circ}\) and \(x = 107^{\circ}\), then \(\angle A=180^{\circ}-107^{\circ}=73^{\circ}\).

Answer:

\(73\)