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?

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:

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?

Which of the following statements is/are correct?

A. A triangle can have all angles less than 60°.

B. A triangle can have one obtuse angle.

C. A triangle can have two right angles.

D. A triangle can have two acute angles.

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

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

ΔABC and ΔDEF are congruent triangles respectively. If AB = 6 = DE, BC = 8 = EF and m ∠B = 30°, then m ∠D + m ∠C =_________.

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 :

In the given triangle, CD is the bisector of ∠BCA. CD = DA. If ∠BDC = 76º, what is the degree measure of ∠CBD?

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 ΔABC, AB = AC, O is a point on BC such that BO = CO and OD is perpendicular to AB and OE is perpendicular to AC. If ∠BOD = 60°, then measure of ∠AOE is:

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

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

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

From the circumcentre L of triangle △XYZ, perpendicular LM is drawn on side YZ. If ∠YXZ= 60° then the measure of ∠YLM is:

From the following figure find x + y + z.

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

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:

In a ∆ABC, the internal bisectors of the angle B and the angle C intersect at an angle of 105°. What is the value of the angle A?

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

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:

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

If the angles of a triangle are in the ratio of 2:3:7, then find the ratio of the greatest angle to the smallest angle.

PQR is a triangle. The bisectors of the internal angle ∠Q and external angle ∠R intersect at S. If ∠QSR = 40°, then ∠P is:  

If the angles of a triangle are in the ratio of 2 : 5 : 8, then find the value of the smallest angle.

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

If two complete angles are in the ratio of 2 : 3, find the ratio of square of smaller angle to the square of the greater angle.

If two complementary angles are in the ratio 4 : 5, find the greater angle.

If S is the midpoint of a straight line PQ and R is a point different from S, such that PR = PQ, then which of the following is true?

PQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. The measure of \(\frac 1 2 \)∠PSQ is :

In ∆ABC, the bisectors of angle ABC and angle ACB intersect each other at point O. If the angle BOC is 125°, then the angle BAC is equal to:

In a ∆PQR and ∆ ABC, ∠P = ∠A and AC = PR. Which of the following conditions is true for triangle PQR and ABC to be congruent?

Two circles touch each other externally at C. AB is a direct common tangent to the two circles, A and B are points of contact; and ∠CAB = 55°. Then ∠ACB is:

In a ΔPQR,∠P : ∠Q : ∠R = 3 ∶ 4 ∶ 8. The shortest side and the longest side of the triangle, respectively, are:

E, F, G, and H are four points lying on the circumference of a circle to make a cyclic quadrilateral. If ∠FGH = 57°, then what will be the measure of the ∠HEF?

If the angles of a triangle are in the ratio 1 : 4 : 7, then the ratio of the greatest angle to the smallest angle.

Let ABC, and PQR be two congruent triangles such that ∠A = ∠P = 90 °. If BC = 17 cm, PR = 8 cm, find AB (in cm).

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

If (7x + 5)° and (x + 5)° are complementary angles, then find the value of x.

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

In a triangle ABC, side BC is produced to D such that ∠ACD = 127º. If ∠ABC = 35º, then find ∠BAC.

△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.

In a triangle, PQR, QR is produced to S. If ∠PRS = (9x - 15)°,  ∠RPQ = (2x)°, and ∠PQR = (4x + 15)°, what is the value of x?

Minor arc BC subtends angle BAC and BDC at points A and D. respectively, on the circumference in the major sector of the circle with center O. What is the value (in degrees) of (∠ABC + ∠ACB) if ∠BDC = 73°

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.

AB is the chord of the circle, and AOC is its diameter, such that ACB = 65º. If AT is the tangent to the circle at point A, then angle BAT is equal to:

If m∠C = m∠Z and AC = XZ, then which of the following conditions is necessary for ΔABC and ΔXYZ to be congruent?

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

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.