In the given figure, from the point P two tangents PA and PB are drawn to a circle with centre O and radius 5 cm. From the point O, OC and OD are drawn parallel to PA and PB respectively. If the length of the chord AB is 5 cm, then what is the value (in degrees) of ∠COD?

In ΔABC, AB and AC are produced to points D and E, respectively. If the bisectors of ∠CBD and ∠BCE meet at point O, so that ∠ BOC = 76°, then find the measure of ∠A.

AB and BC are two chards of a circie with centre O. Both chords are on either side of the centre O. Point A and point C are connected to the centre O, such that \(\angle\)BAO=36° and \(\angle\)BCO=40°. What is the degree measure of the angle subtended by the minor arc AC at the centre O?

In ∆ABC, ∠BAC = 60°, and O is a point inside ∆ABC. If ∠OBC is two times ∠OBA and ∠OCB is two times ∠OCA, then what will be the measure of ∠BOC?

In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at point T (inside the quadrilateral) and ∠STR = 32.5°. If the ratio of ∠P to ∠Q is 4 : 9, then what is the difference between the measures of ∠Q and ∠P?

In the given figure, MNP, SQP, NQR, and MSR are straight lines. ∠NPQ= 54° and ∠QRS = 68°. What is the degree measure of ∠SMN?

In cyclic quadrilateral ABCD, sides AB and DC, when produced, meet at E and sides AD and BC, when produced, meet at F. If ∠AFC= 21° and ∠BEC = 49°, then what is the measure of ∠BAD?

Three sides of a ∆PQR are QR = 35, PR = 48, and PQ = 49. The internal bisector of ∠Q meets PR at T, and the bisector passes through in Centre I. The ratio of QI : IT is:

In ∆ABC, H is the orhocenter and I is the incentre for the given, if ∠BIC - ∠BHC = 21°, then find ∠BOC (if O is the circumcentre of ∆ABC)?

In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at point T (inside the quadrilateral) and ∠STR = 32.5°. If the ratio of ∠P to ∠Q is 4 : 9, then what is the difference between the measures of ∠Q and ∠P?

The circumcentre of a ΔABC is O. If \(\angle \)BAC = 70°  and \(\angle \)BCA = 80°, then the measure of \(\angle\)OAC is equal to:

Given that ∆MAN and ∆CPT are congruent to each other, such that ∠M = 75°, ∠N = 65°, ∠A = 40°, ∠C = x/2, ∠P = 6y + 16. Find the value of (x – 5y).

In the given figure, O is the centre of the circle ∠BCA = 50°. The value of ∠BDA is:

In ΔDEF , DE = 12 cm, EF = 15 cm, and ∠DEF = 90°. ΔDEF is congruent to ΔXYZ. If YZ = 15 cm, then what is the length of XZ?

Select the most appropriate option to fill in the blank.

The angles are equal, consequently the sides are _____________.

AP and AQ are two tangents drawn to a circle with centre O from an external point A. If ∠PAQ = 40°, then ∠POQ is:

In a rhombus STUV, S and U are joined ∠ SUV = 44°, ∠STU = 92°, what is the degree measure of 4 ∠SVU - 3∠TSU?

In a cyclic quadrilateral ABCD, the ratio of angle A and B is 1 : 2 and the ratio of angle C and D is 5 : 4. What is the value of ∠ A?

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

In the figure shown above, quadrilateral PQRS has its vertices on the circumference of the circle with centre O. If m∠QOS =20x° and m∠ QRS = 26x°, then what is the value of ‘x’?

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 ∆ABC and ∆PQR, AB = 7 m, BC = 8 m, AC = 9 m, PQ = 7 m, QR = 8 m and PR = 9 m. Which of the following is true for these triangles?

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 a circle, O is the center and AOB is the diameter. AT is a tangent to the circle. Line TB intersects the circle at Q. Given that ∠AOQ = 94°, find ∠ATQ.

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°.

Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact, and ∠PAB = 40° . The measure of ∠ABP is:

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

AB is the diameter of a circle with the center O. P as a point on it. If ∠AOP = 95° then find ∠OBP ?

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

In a circle with centre O, PQR is a tangent at the point Q on it. AB is a chord in the circle parallel to the tangent such that ∠BQR = 70^o. What is the measure of ∠AQB?

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

If PQ and PR are the two tangents to a circle with center O, and ∠QOR=150°, then ∠QPR is equal to:

PS and PT are two tangents from a point P outside the circle with center O. If S and T are points on the circle such that ∠SPT = 130°, then the degree measure of ∠OST is equal to:

PBA and PDC are two secants. AD is the diameter of the circle with the centre at O. ∠A = 30°, ∠P = 20°. Find the measure of ∠DBC.

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

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

In ΔPQR,PQ = QR and O is an interior point of ΔPQR such that ∠OPR = ∠ORP. Consider the following statements:

(i) ΔPOR is an isosceles triangle.

(ii) O is the centroid of ΔPQR.

(iii) ΔPQO is congruent to ΔRQO.

Which of the above statements are correct?

An angle is 30° more than one-half of its complement. Find the difference between the greater and the smaller angles.

A quadrilateral PQRS is inscribed in a circle of centre O, such that PQ is a diameter and \(\angle PSR=120°\) . Find the value of \(\angle QPR\).

A, B, C are three angles of a triangle. If A - B = 45° and B - C = 15° then ∠A = ?

If angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, find the largest angle.

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

In the figure given below, PM ⟂ AL and ∠PMO = 40º. Find ∠LHS + reflex ∠MAH.

Two angles are supplementary angles. One of the angles is 18° less than twice of other. Find both angles.

In an isosceles triangle ABC, the bisector of equal angles ∠B and ∠C meets at O inside the triangle. If ∠BOC = 164°, then find the sum of (∠A + ∠OBC) 

In triangle MNO, ∠M = (4x - 10°), ∠N = (5x - 5°) and ∠O = (3x + 15°). Find ∠N - ∠O.

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?

If x and y are the complementary angles and m and n are supplementary angles, if x = 60° and m = 120°, then find the sum of y and n.

In the given figure, from an external point C, tangents CA and CB are drawn to a circle with center O. If ∠AOB = 220° (bigger arc of the circle), then find ∠CAB.

The ratio of the five angles of a pentagon is 2 : 3 : 4 : 4 : 5. What would be the measure of the smallest angle?