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 \(n = 5\) (a pentagon), the sum \(S=(5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Let the interior angle adjacent to \(\angle A\) be \(x\). Then \(x+\angle A = 180^{\circ}\) (linear - pair of angles).

The sum of the known interior angles is \(96^{\circ}+118^{\circ}+104^{\circ}+115^{\circ}+x=540^{\circ}\).
First, calculate \(96 + 118+104 + 115=433\). So \(433^{\circ}+x = 540^{\circ}\).
Then \(x=540^{\circ}-433^{\circ}=107^{\circ}\).

Step3: Find \(\angle A\)

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

Answer:

\(73\)