The adjacent angles on a straight line are in the ratio 5 ∶ 4, then the smaller angle is –

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:

Two chords AB and CD of a circle with centre O intersect at P. If ∠APC = 40°. Then the value of ∠AOC + ∠BOD is

The area of a rhombus is 144 square units. The length of one of its diagonals is twice the length of other diagonal. What is the sum of length of its diagonals?

If one of the equal angles of an isosceles triangle is 65°, then the angle at the vertex is

In a circle with centre O, AB is the diameter. P and Q are two points on the circle on the same side of the diameter AB. AQ and BP intersect at C. If ∠POQ = 54°, then the measure of ∠PCA is:

AB is diameter of a circle with centre 'O'. CD is a chord which is equal to the radius of the circle. AC and BD are extended so that they intersect each other at point P. Then find the value of ∠ APB.

The two vowels touch each other internally. Their radii are 2 cm and 3 cm. What will be the length of the largest chord of the bigger circle outside the inner circle?