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

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

The following is a figure of a polygon that has 6 sides. Find the external angle y of the polygon as shown in the figure.

If ΔABC is congruent to ΔDEF, then EF = _________.

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

ABCD is a cyclic quadrilateral and BC is the diameter of the related circle on which A and D also lie. ∠BCA = 19° and ∠CAD = 32º. What is the measure of ∠ACD?

O is the incentre of the triangle PQR. If angle POR = 140 degree, then what is the angle PQR?

It is given that ∆ABC ≅ ∆PQR, AB = 5 cm, ∠B = 40°, and ∠A = 80°. Which of the following options is true?
 

Triangle PQR is inscribed in a circle such that P, Q and R lie on the circumference. If PQ is the diameter of the circle and ∠PQR = 40°, then what is the value (in degrees) of ∠QPR?

In a triangle ABC, AB = AC. BC is extended to D such that CD = AB and the angle ADC is 30°. What are the angles of triangle ABC?

PQRS is a cyclic quadrilateral. If ∠P is three times of ∠R and ∠S is four times of ∠Q, then the sum of ∠S + ∠R will be:

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 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 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.

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 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 the given figure ∠POA = (3x + 72°), ∠POQ = (2x - 3°), and ∠QOB = (x - 3°) then, find the value of ∠BOQ.

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?

Find the supplementary angles:

(i) 60º and 30º

(ii) 149º and 31º

(iii) 91º and 89º

(iv) 120º and 240º

In the given figure EF || GH, AB, and CD are the transversals. If ∠NMP = (70° + x) and ∠HOD = 2x then, find the value of ∠HOD. 

If in the given figure ∠OGL = ∠OCB and ∠LGP = 135°and ∠BOG = 75° then, find ∠OBC.

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?

‘X’ is the circumcentre of angle PQR. A perpendicular drawn from ‘X’ meets QR at point ‘S’. If angle QPR = 75^o, then find the measure of ∠QXS.

If ABCDEF is a regular hexagon, then what is the value (in degrees) of ∠ADB?

PQ is a diameter of a circle with centre O. The tangents at R meets PQ produced at A. If ∠RPQ = 27°, then measure of ∠RQP is:

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

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

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

PQRS is a cyclic quadrilateral. If ∠P is three times of ∠R and ∠S is four times of ∠Q, then the sum of ∠S + ∠R will be:

It is given that ∆ABC ≅ ∆PQR, AB = 5 cm, ∠B = 40°, and ∠A = 80°. Which of the following options is true?
 

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

If in △ABC, AB = AC and ∠ACD = 125°, then ∠BAC is:

In a given figure, O is the centre of the circle and ∠POQ = 54°. What is the measure (in degrees) of ∠PRQ?

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?

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 a circle, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD outside of the circle, and BA is produced to F. If ∠ABC = 85° and ∠FAE = 24°, find the value of ∠BCD.

In the given figure two circles touches internally at P . ∠APB = 110° and ∠DPC = 78°, then find ∠APD ?

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?

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 \(\angle QPR\).

Side BC of a ΔABC is produced to D such that CD = AC. Also, AD = BD and AB = AC. What is the measure of ∠ADB?

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.

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

In a circle, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD outside of the circle, and BA is produced to F. If ∠ABC = 85° and ∠FAE = 24°, find the value of ∠BCD.

In an isosceles triangle, the angle between equal sides is 40°. The bisectors of the other two angles will intersect each other at an angle of:

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

In a triangle ABC, AB = AC. BC is extended to D such that CD = AB and the angle ADC is 30°. What are the angles of triangle ABC?

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

The measure angles of the triangle are in arithmetic progression with a common difference of 40°. Find the measure angles of the triangle.

△PQR and △SQR are both isosceles triangles on a common base QR such that P and S lie on the same side of QR. If ∠QSR = 60° and ∠QPR = 100°. then find ∠SRP.