Question

18. In the figure, o is the center of the circle passing through P, Q, R and S. If angle SOQ = 150°, find the values of x and y.

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Answer 1

x = 75°

y = 105°

Explanation:

Angle subtended on the circumference of the circle is half of the angle subtended on the center of the circle.

`\therefore m\angle SRQ = (1)/(2) * m\angle SOQ\\\\</p><p>\therefore x = (1)/(2) * 150\degree \\\\</p><p>\red{\bold{\therefore x =75\degree}} \\`

Quadrilateral PQRS is a cyclic quadrilateral.

`\therefore m\angle R + m\angle P= 180\degree \\\\</p><p>\therefore x + y = 180\degree \\\\</p><p>\therefore 75\degree + y = 180\degree \\\\</p><p>\therefore y = 180\degree - 75\degree \\\\</p><p>\purple {\bold {\therefore y = 105\degree}} \\`