In the given figure ∠APB = 33°, find the value of \(\sqrt{{1\over3}{{\times∠AOB}}}\).

In ∆ABC, the internal bisectors of ∠ABC and ∠ACB meet at X and ∠BAC = 30°. The measure of ∠BXC is:

In the triangle ABC, find the exterior angle to A if the interior angle to B is 60° and the exterior angle to C is 150°.

In the given figure ∠AOP = 90°, ∠AOB = ∠COD = x, and ∠BOC = ∠DOQ = 2x. Examine the figure and find the measure of ∠BOD.

Given is a circle with centre at C. A, B and D are the points on the circumference. Find ∠ABC.

Let ABC and PQR be two congruent triangles, such that ∠A = ∠P = 90°. If BC = 29 cm, PR = 21 cm, find the value (in cm) of AB.

The measures of two angles of a triangle are in the ratio 3 : 7. If the sum of these two measures is equal to the measure of the third angle, then find the smallest angle.

If △XYZ ≅ △LMR, then m + x + p = _________________.

In the given figure, QS and RS are two tangents to the circle with center O. If ∠QSR = 80°, then what is the value of ∠QPR?

A trapezium ABCD is such that all four points lie on a circle. One of the parallel sides of the trapezium (AB) is the diameter of the circle. If CAB = 40°, find the value of CAD.

In the given figure, if AC and DE are parallel and ∠CAB = 38˚, then the value of ∠ABC + 4∠CBD is: 

If the angles of a quadrilateral are in the ratio of 4 : 9 : 11 : 12 , then find the smallest of the angles (in degrees).

In the given figure, O is the center of a circle, CD is a chord and CM is the tangent at C. If ∠COD = 120°, then calculate ∠DCM.

If O is the ortho centre of ΔABC and ∠BOC = 100°, the measure of ∠BAC is?

In ΔABC, D is a point on AC such that AB = BD = DC, if ∠BAD = 70°, then the measure of (∠B + ∠C) is:

Consider a triangle PQR, right-angled at R, in which PQ = 29 units, QR = 21 units, and ∠PQR=θ. Find the value of cos⁡²θ − sin⁡²θ.

In a triangle PQR, incentre is A and ∠QAR = 116°. Find the measure of ∠QPR.

In a △ABC, the internal bisectors of ∠B and ∠C meet at O. If ∠BAC = 72°, then the value of ∠BOC is:

If O is the ortho centre of ΔABC and ∠BOC = 100°, the measure of ∠BAC is?

Let ABC and PQR be two congruent triangles, such that ∠A = ∠P = 90°. If BC = 29 cm, PR = 21 cm, find the value (in cm) of AB.

In a ΔPQR, the bisectors of P and R meet at a point M inside the triangle. If the measurement of ∠PMR is 127°, then the measurement of ∠Q is:

In ΔPQR, if 4∠P = 5∠Q = 20∠R, then the value of ∠Q is:

ΔABC and ΔDEF are two triangles such that ΔABC ≅ ΔFDE. If AB=17 cm, ∠B=52° and ∠A=95°, then which of the following options is true?

In the triangle ABC, find the exterior angle to A if the interior angle to B is 60° and the exterior angle to C is 150°.

If the angles of a quadrilateral are in the ratio of 4 : 9 : 11 : 12 , then find the smallest of the angles (in degrees).

In the following figure, AB and CD are the diameters of the circle. If ∠AOD = 80°, then what is the value of ∠ADC?

In a hexagon, the exterior angles are in arithmetic progression with a common difference of 10°. What is the value of the smallest exterior angle?

In the diagram above, TU || PS and Points Q and R lie on PS. Also ∠PQT = x°, ∠RQT = (x − 60)°,and ∠TUR = (x + 50)°. What is the measure of ∠URS?

In the given figure ∠AOP = 90°, ∠AOB = ∠COD = x, and ∠BOC = ∠DOQ = 2x. Examine the figure and find the measure of ∠BOD.

O is the centre of a circle, and A is a point on a major arc BC of the circle. ∠BOC and ∠BAC are the angles made by the minor arc BC on the centre and circumference, respectively. If ∠ABO = 40° and ∠ACO = 30°, then find ∠BOC.

In the given figure, \(\Delta\)QPS \(\approx\) \(\Delta\)SRQ. Find the measure of \(\angle\)PSR.

In the shown figure, BC is a chord and CD is a tangent through the point C. If ∠AOC = 112°, then find ∠ACD.

Let ABC and PQR be two congruent triangles, such that ∠A = ∠P = 90°. If BC = 29 cm, PR = 21 cm, find the value (in cm) of AB.

In the given figure, 'G' is the centre of the circle. Find the angle ACB.

An equilateral triangle ABC surmounts a square BCDE. The value of ∠EAB + 3∠AEB is

In the given figure CD || AB, ∠CBA = 35°. Find the value of ∠CDB - ∠DBC.

If 45° and 65° are the angles of a triangle, then find the exterior angle of the third angle (remaining angle).

If ΔBPQ ≅ ΔASR and  ∠A = \(\frac{1}{3}\)∠R = ∠S, then find  ∠Q. (All angles are in degrees).

In a hexagon, the exterior angles are in arithmetic progression with a common difference of 10°. What is the value of the smallest exterior angle?

In the given figure AB = DB and AC = DC. If ∠DBC = (2x - 4)° and ∠ABD = 58°, ∠ACB = (y + 15)° and ∠DCB = 63°, then the value of 2x + 5y is :

There are two complementary angles. The larger angle is 2 times and 5° more than the smaller angle. Find both angles.

In the given figure, QS and RS are two tangents to the circle with center O. If ∠QSR = 80°, then what is the value of ∠QPR?

In the given figure, ∠SPQ = 85° and ∠PRS = 20° then what is the value of ∠PSQ?

If the difference between two complementary angles a and b is 60° then, find the value of (2a - b).

In the given figure ∠APB = 33°, find the value of \(\sqrt{{1\over3}{{\times∠AOB}}}\).

Two circles touch each other externally at P. AB is a direct common tangent to the two circles. If A and B are points of contact and PAB = 65°, then ABP is:

If the angles of a triangle are in the ratio of 9 ∶ 11 ∶ 16, then the difference between the greatest angle and the smallest angle is:

In the adjoining figure line l is parallel to m. What is the value of 2x + y?

In the given figure ∠AOP = 90°, ∠AOB = ∠COD = x, and ∠BOC = ∠DOQ = 2x. Examine the figure and find the measure of ∠BOD.

In the given figure, O is the center of a circle, CD is a chord and CM is the tangent at C. If ∠COD = 120°, then calculate ∠DCM.