CAIE IGCSE Mathematics Extended E4.7.1 Calculate Unknown Angles and Give Explanations Using the Following Questions

Find unknown angles using circle properties: the angle in a semicircle and the radius–tangent angle are 90°, centre and circumference angles are linked, and cyclic quadrilaterals and the alternate segment theorem give further relationships. Give the theorem that justifies each step.

Exam points

Use the angle in a semicircle and the perpendicular angle between a radius and tangent to identify 90° angles.
Relate angles at the centre and circumference, and use equal angles in the same segment.
Use supplementary opposite angles in cyclic quadrilaterals and the alternate segment theorem, giving the circle theorem used.

[Maximum number: 3]

NOT TO SCALE

The diagram shows a cyclic quadrilateral ABCD. BD and AC intersect at X.

(a)

Angle $B A D=74^{\circ}$ and angle $B C A=34^{\circ}$ .

Find

[ 3 ]

(i)

angle BDA

Angle B D A=

[ 1 ]

(ii)

angle BCD

Angle B C D=

[ 1 ]

(iii)

angle ABD.

Angle A B D=

[ 1 ]

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CAIE IGCSE Mathematics Extended E4.7.1 Calculate Unknown Angles and Give Explanations Using the Following Questions question 1

Question (a)

Question (i)

Question (ii)

Question (iii)