Are you looking for solution of Class 10 ICSE Important Maths Questions for 2026 Exams? Here you’ll find complete, step-by-step solutions for every question. Designed for both students and teachers, these answers make board exam revision easier with clear explanations, formula highlights, and downloadable PDF options.
Q1: In the adjoining diagram, O is the centre of the circle and PT is the tangent. Find the value of x.+1
Solution: Let the line segment QOT form a straight line passing through the center O. We are given $\angle QOP = 110^\circ$.
Step 1: Find $\angle POT$.
Since QOT is a straight line, the angles form a linear pair and add up to 180°.
$$\angle POT = 180^\circ – \angle QOP$$
$$\angle POT = 180^\circ – 110^\circ$$
$$\angle POT = 70^\circ$$
Step 2: Apply the tangent-radius theorem.
A tangent to a circle is always perpendicular to the radius at the point of contact. Therefore, radius OP is perpendicular to tangent PT.
$$\angle OPT = 90^\circ$$
Step 3: Apply the angle sum property in $\Delta OPT$.
The sum of all interior angles in a triangle is 180°.
$$\angle POT + \angle OPT + \angle PTO = 180^\circ$$
$$70^\circ + 90^\circ + x = 180^\circ$$
Step 4: Simplify and solve for x.
$$160^\circ + x = 180^\circ$$
$$x = 180^\circ – 160^\circ$$
$$x = 20$$
Final Answer: The value of x is 20.