A pair of tangents can be constructed to a circle inclined at an angle of \(170^\circ\).
Step 1: When two tangents are drawn from an external point to a circle, they meet at some angle. Let this angle be \(\theta\).
Step 2: The angle between the two radii drawn to the points of contact is always the supplementary angle of \(\theta\). That means, angle between the radii = \(180^\circ - \theta\).
Step 3: Here, \(\theta = 170^\circ\). So, angle between radii = \(180^\circ - 170^\circ = 10^\circ\).
Step 4: A \(10^\circ\) angle at the centre of a circle is possible in geometry (it is a very small but valid angle).
Final Step: Therefore, it is possible to construct such a pair of tangents to the circle.