AnglesAngles

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Cat1Cat1 Cat2Cat2 Cat3Cat3 Cat4Cat4 Cat5Cat5

a = 50 b = 110a = 50 b = 110

Cat1 for $100

Find the size of angle a and angle b

(a)(a)112112°° corresponding anglescorresponding angles(b)(b) 5050°°

Cat1 for $200

(a) Find angle x and give a reason for your answer.

(b) Find angle y

3030°°

Cat1 for $300

Work out the size of angle x

x = 40 y = 140x = 40 y = 140

Cat1 for $400

Find the size of angle x and angle y

1616°°

Cat1 for $500

Find the size of angle OBC

135135°°

Cat2 for $100

Find the size of angle a

p = 54p = 54° q = 40°° q = 40°

Cat2 for $200

Find the size of angle p and angle q

Kite 2 since opposite anglesKite 2 since opposite anglesTotal 180Total 180°°

Cat2 for $300

Which of the kites below is a cyclic quadrilateral? Give a reason for your answer.

Angle DAB = 90˚ (Tangent meets radius at right-angle)Angle DAB = 90˚ (Tangent meets radius at right-angle)So angle ABD = 50˚ since angles in a triangle total 180˚So angle ABD = 50˚ since angles in a triangle total 180˚Triangles DAB and DCB are congruent so Triangles DAB and DCB are congruent so Angle ABC is 100˚Angle ABC is 100˚

Cat2 for $400

x = 65x = 65° y = 130°° y = 130°

Cat2 for $500

Find the size of angle x and angle y

r = 72r = 72° s = 55°° s = 55°

Cat3 for $100

Find the size of angle r and angle s

a = 50a = 50° b = 70°° b = 70°

Cat3 for $200

Find the size of angle a and angle b

120120°°

Cat3 for $300

Work out the size of angle x

p = 140p = 140° q = 70°° q = 70°

Cat3 for $400

Find the size of angle p and angle q

OSR = 90OSR = 90°° and and OSQ = 50OSQ = 50°° QSR = 40QSR = 40°°Since angle QSR = angle QRS Since angle QSR = angle QRS QSR is an isosceles triangleQSR is an isosceles triangle

Cat3 for $500

Prove that triangle QSR is isosceles

Z = 110Z = 110°°Opposite angles in a cyclic quadrilateralOpposite angles in a cyclic quadrilateral

Total 180Total 180°°

Cat4 for $100

Find the size of angle z.Give a reason for your answer.

3030°°

Cat4 for $200

Find the size of angle x

x = 100x = 100° (Angle at Centre)° (Angle at Centre)y = 130y = 130° (Cyclic Quadrilateral)° (Cyclic Quadrilateral)z = 70z = 70° (Angle in Semi-Circle)° (Angle in Semi-Circle)

Cat4 for $300

Find the size of angles x, y and z.Give reasons for your answers.

4545°°

Cat4 for $400

Here is a regular octagon. Find the size of angle y.Give a reason for your answer.

x = 15x = 15° EAD = 120° ° EAD = 120°

Cat4 for $500

Find the size of x and angle EAD

Y = 100Y = 100°°Angle at the centre is double the angle atAngle at the centre is double the angle atthe circumference subtended by the radiithe circumference subtended by the radii

Cat5 for $100

Find the size of angle y.Give a reason for your answer.

125125°°

Cat5 for $200Find the size of angle x

x = 65x = 65° y = 25°° y = 25°

Cat5 for $300

Find the size of angle x and angle y

BAT = 62BAT = 62° and ABC = 71°° and ABC = 71°Tangents and Alternate Segment TheoremTangents and Alternate Segment Theorem

Cat5 for $400

Find the size of angles BAT and ABCWhich circle theorems did you use?

62

6271

71

x = 124x = 124°° y = 42 y = 42°°

Cat5 for $500

Find the size of angle x and angle y