Question

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Explanation:

Step1: Find the unknown angle in the first triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the unknown angle in the first triangle be \(x\).
\(x + 48^{\circ}+65^{\circ}=180^{\circ}\)
\(x=180^{\circ}-(48^{\circ} + 65^{\circ})\)
\(x = 67^{\circ}\)

Step2: Use the linear - pair and angle - sum properties

The angle adjacent to \(x\) (from step 1) and the \(50^{\circ}\) angle forms a linear - pair with the angle at the common vertex of the two triangles. Let the common - vertex angle be \(y\).
Since \(x = 67^{\circ}\), and \(x+50^{\circ}+y=180^{\circ}\) (straight - line angle), then \(y=180^{\circ}-(67^{\circ}+50^{\circ}) = 63^{\circ}\)

Step3: Find the unknown angle in the second triangle

Let the unknown angle in the second triangle be \(z\).
Using the angle - sum property of a triangle (\(z + 35^{\circ}+y=180^{\circ}\))
Substitute \(y = 63^{\circ}\) into the equation: \(z+35^{\circ}+63^{\circ}=180^{\circ}\)
\(z=180^{\circ}-(35^{\circ}+63^{\circ})\)
\(z = 82^{\circ}\)

Answer:

\(82^{\circ}\)