Question

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Explanation:

Step1: Find the adjacent angle of \(35^{\circ}\)

Since the sum of adjacent angles on a straight line is \(180^{\circ}\), the adjacent angle of \(35^{\circ}\) is \(180 - 35=145^{\circ}\)

Step2: Use the exterior - angle property of a triangle

The exterior - angle property of a triangle states that the exterior angle is equal to the sum of the two non - adjacent interior angles. Let the unknown angle be \(x\). Then \(x + 100=145\)

Step3: Solve for \(x\)

Subtract \(100\) from both sides of the equation \(x + 100=145\). So \(x=145 - 100 = 45^{\circ}\)

for the second problem (assuming it's another angle - finding problem using angle properties):

Step1: Find the adjacent angle of \(155^{\circ}\)

The adjacent angle of \(155^{\circ}\) (on a straight line) is \(180 - 155 = 25^{\circ}\)

Step2: Use the exterior - angle property of a triangle

Let the unknown angle be \(y\). By the exterior - angle property \(y=25 + 60\)

Step3: Calculate \(y\)

\(y=85^{\circ}\)

Answer:

For the first problem, the angle is \(45^{\circ}\). For the second problem (assuming the above steps are for it), the angle is \(85^{\circ}\)