Points $P, Q, R, S$ lie consecutively on a circle, forming a cyclic quadrilateral. Angle $∠ P QR = 2 x + 1 5^{\circ}$ and angle $∠ P S R = 3 x - 1 0^{\circ}$ . Find the value of $x$ .

Practise more Geometry, Trigonometry and Circle Theorems.

Free questions with an explanation for every one, and full timed UK GCSE mock tests.

All Geometry, Trigonometry and Circle Theorems questions Take a mock test

More Geometry, Trigonometry and Circle Theorems questions

$A, B, C$ are points on the circumference of a circle with centre $O$ . Angle $∠ A O C = 13 0^{\circ}$ . What is the size of angle…
In a triangle $X Y Z$ , $X Y = 7 cm, Y Z = 9 cm$ , and angle $∠ X Y Z = 4 8^{\circ}$ . Calculate the area of triangle $X Y Z$ to 1 deci…
In triangle $A B C$ , side $a = 6 cm, b = 10 cm$ , and angle $C = 12 0^{\circ}$ . Calculate the length of side $c$ .
$A$ and $B$ are mathematically similar cylinders. Cylinder $A$ has surface area $36 cm^{2}$ and Cylinder $B$ has surface area…
$T A$ is a tangent to a circle at point $A$ . $A B C$ is a triangle inscribed in the circle. If angle $∠ T A B = 6 8^{\circ}$ and angle…
A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. What is the length of the other short side?