Find the nature of roots of 2x2 + 3x + 5 = 0. Give an example for (i) Similar Figures and (ii) Non-Similar Figures.

Step 1: Identify the properties of tangents and radii. Given that TP and TQ are tangents to a circle with center O, the radii OP and OQ are perpendicular to the tangents at the points of tangency P and Q, respectively. Therefore, we have: $\angle OPT = 90^\circ$ $\angle OQT = 90^\circ$

Step 2: Use the sum of angles in a quadrilateral. The points O, P, T, and Q form a quadrilateral OPTQ. The sum of the interior angles of a quadrilateral is $360^\circ$. So, we can write the equation: $\angle OPT + \angle PTQ + \angle OQT + \angle POQ = 360^\circ$

Step 3: Substitute the known values into the equation. We are given $\angle POQ = 110^\circ$. Substituting the known angles: $90^\circ + \angle PTQ + 90^\circ + 110^\circ = 360^\circ$

Step 4: Solve for $\angle PTQ$. Combine the constant terms: $290^\circ + \angle PTQ = 360^\circ$ Subtract $290^\circ$ from both sides: $\angle PTQ = 360^\circ - 290^\circ$ $\angle PTQ = 70^\circ$

The value of $\angle PTQ$ is $\boxed{70^\circ}$.