In the diagram, DEF is a cyclic quadrilateral with DE || GF - NSC Mathematics - Question 9 - 2022 - Paper 2
Question 9
In the diagram, DEF is a cyclic quadrilateral with DE || GF. DE is produced to R. T is another point on the circle. EG, FT and ET are drawn. \( \hat{E_4} = 72^\circ ... show full transcript
Worked Solution & Example Answer:In the diagram, DEF is a cyclic quadrilateral with DE || GF - NSC Mathematics - Question 9 - 2022 - Paper 2
Step 1
9.1.1 Determine \( \hat{DGF} \)
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Answer
Using the property of cyclic quadrilaterals, we know that the exterior angle is equal to the interior opposite angle. Thus, ( \hat{DGF} = \hat{E_4} = 72^\circ ).
Step 2
9.1.2 Determine \( \hat{T} \)
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Answer
Since ( G_1 = 16^\circ ) and both angles are in the same segment of the circle, we have ( \hat{T} = \hat{G_2} = 56^\circ ).
Step 3
9.1.3 Determine \( \hat{GEF} \)
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Answer
Using alternate angle properties, since ( \hat{E_4} = 72^\circ ) and ( DE || GF ), we have:
[ \hat{GEF} = 180^\circ - \hat{E_4} = 180^\circ - 72^\circ = 108^\circ. ]
