1. 5
Angles in rhombus
The diagram shows a rhombus ABCD where diagonals AC and BD intersect at E.
The diagonal BD is produced to F such that AD = DF. If A 𝐵 E = 68°,
calculate
(i) B 𝐶 D,
(ii) D 𝐴 F,
(iii) E 𝐴 F.
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2. i C 𝐵 D = A 𝐵 D (diagonal BD of rhombus bisects A 𝐵 C) = 68°
B 𝐶 D + A 𝐵 D + C 𝐵 D = 180° (int. ∠s, AB // DC)
B 𝐶 D + 68° + 68° = 180°
B 𝐶 D = 180° – 68° – 68°
= 44°
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3. ii A 𝐷 B = 68° (base ∠s of isos. ∆ABD; or alt. ∠s, AD // BC)
D 𝐴 F + A 𝐹 D = 68° (ext. ∠ of ∆ADF)
D 𝐴 F = A 𝐹 D = 68° 2 (base ∠s of isos. ∆ADF)
= 34°
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4. iii
A 𝐸 F = 90° (diagonals of rhombus bisect each other at right angles)
E 𝐴 F + A 𝐸 F + A 𝐹 E = 180° (∠ sum of ∆AEF)
E 𝐴 F + 90° + 34° = 180°
E 𝐴 F = 180° – 90° – 34°
= 56°
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