Question

find the value of c. 37. ( c^{circ}=? ) ( 72^{circ} ) ( 73^{circ} ) ( 107^{circ} ) ( 253^{circ} )

Explanation:

Step1: Find the adjacent interior angle of \(145^{\circ}\)

The sum of adjacent angles on a straight line is \(180^{\circ}\). Let the adjacent interior angle be \(x\). Then \(x = 180^{\circ}- 145^{\circ}=35^{\circ}\)

Step2: Find the adjacent interior angle of \(108^{\circ}\)

Let the adjacent interior angle be \(y\). Then \(y = 180^{\circ}-108^{\circ} = 72^{\circ}\)

Step3: Use the exterior - angle property of a triangle

The exterior - angle property of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the exterior angle be \(c\). Then \(c=(x + y)\) (where \(x = 35^{\circ}\) and \(y = 72^{\circ}\))
\(c=35^{\circ}+72^{\circ}=107^{\circ}\)

Answer:

\(107^{\circ}\)