Circles / polygons / angles / parallel lines 1

Transcription

1 1) ircles / polygons / angles / parallel lines 1 24 T, and are points on a circle, centre. T is a tangent to the circle at and T is a straight line. is a diameter and angle T = 24. alculate (a) angle T, nswer(a) ngle T = [2] (b) angle, nswer(b) ngle = [1] (c) angle. nswer(c) ngle = [1]

2 ircles / polygons / angles / parallel lines 1 2) x 52 straight line intersects two parallel lines as shown in the diagram. Find the value of x. nswer x = [1] 3) (a) Points, and lie on the circumference of the circle shown above. When angle is 90 write down a statement about the line. nswer(a) [1]

3 ircles / polygons / angles / parallel lines 1 (b) 54 D is the centre of a circle and the line is a tangent to the circle at. D is a point on the circumference and angle D = 54. alculate angle D. nswer(b) ngle D = [3] 4) (a) p 140 D The diagram shows a triangle with extended to D. = and angle D = 140. Find the value of p. nswer(a) p = [2]

4 ircles / polygons / angles / parallel lines 1 4cont) (b) 72 q Find the value of q. nswer(b) q = [2] (c) x Find the value of x. nswer(c) x = [1] (d) 22 In triangle, angle = 90 and angle = 22. alculate angle. nswer(d) ngle = [1]

5 5) ircles / polygons / angles / parallel lines 1 (a) The table below shows how many sides different polygons have. omplete the table. Name of polygon Number of sides 3 Quadrilateral 4 5 Hexagon 6 Heptagon 7 8 Nonagon 9 [3] (b) Two sides, and, of a regular nonagon are shown in the diagram below. x (i) Work out the value of x, the exterior angle. nswer(b)(i) x = [2] (ii) Find the value of angle, the interior angle of a regular nonagon. nswer(b)(ii) ngle = [1]

6 6) ircles / polygons / angles / parallel lines x Find the value of x. nswer x = [1] 7) x Find the value of x. nswer x = [1]

7 8) ircles / polygons / angles / parallel lines The diagram shows part of a regular polygon with each interior angle 150. alculate the number of sides of the polygon. nswer [3] 9) R 55 Q P, Q and R lie on a circle, centre. PR is a diameter and angle QR = 55. Find (a) angle PQR, P nswer(a) ngle PQR = [1] (b) angle RQ, nswer(b) ngle RQ = [1] (c) angle PQ. nswer(c) ngle PQ = [1]

8 10) ircles / polygons / angles / parallel lines 1 S T 54, and lie on a circle, centre. is a diameter and ST is a tangent at. ngle = 54. Find (a) angle T, nswer(a) ngle T = [1] (b) angle, nswer(b) ngle = [1] (c) angle, nswer(c) ngle = [1] (d) angle. nswer(d) ngle = [1]

9 11) D ircles / polygons / angles / parallel lines w p t M The diagram shows a quadrilateral D with D parallel to. (a) Write down the geometrical name for a quadrilateral with only one pair of parallel sides. nswer(a) [1] (b) M is a straight line and D =. ngle D = 32 and angle = 67. Find the values of p, t and w, giving a reason for each answer. nswer (b) p = because [2] t = because [2] w = because [2]

10 12) ircles / polygons / angles / parallel lines 1 x The diagram shows a quadrilateral. Work out the value of x. nswer x = [1] 13) D 55 y x The diagram shows a circle, centre, with diameter. is a tangent to the circle at and angle D = 55. straight line from meets the circle at D and. alculate the value of (a) x, nswer(a) x = [2] (b) y. nswer(b) y = [1]

11 14) ircles / polygons / angles / parallel lines 1 T In the diagram, TU is a tangent to the circle at. is a diameter of the circle and =. Find (a) angle, U nswer(a) ngle = [1] (b) angle, nswer(b) ngle = [1] (c) angle U. nswer(c) ngle U = [1]

12 ircles / polygons / angles / parallel lines 1 15) 3 S 36 T R The points P, R and S lie on a circle, centre. RT is a straight line and TS is a tangent to the circle at S. ngle ST = 36. P (a) Write down the size of angle TS, giving a reason for your answer. nswer(a) ngle TS = because [2] (b) (i) alculate the size of angle TS. nswer(b)(i) ngle TS = [1] (ii) Show that angle PR = 63. nswer(b)(ii) [2] (c) (i) Write down the size of angle PRS. nswer(c)(i) ngle PRS = [1] (ii) alculate the size of angle PSR. nswer(c)(ii) ngle PSR = [1]