In the figure, sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively. If $∠ C B F = 130^{\circ} a n d ∠ C D E = x^{\circ},$ find the value of x.
(2 Marks)

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Solution

ABCD is a cyclic quadrilateral.
We know that in a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
∴ ∠ CBF = ∠ CDA (1 mark)
⇒ ∠ CBF = (180° – x)
⇒ 130° = 180° – x [∵ ∠ CBF = 130 °]
⇒ x = (180° – 130° ) = 50°
Hence, x = 50° (1 mark)

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In the figure, sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively. If ∠CBF=130∘ and ∠CDE=x∘, find the value of x. (2 Marks)

ABCD is a cyclic quadrilateral. We know that in a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle. ∴ ∠ CBF = ∠ CDA (1 mark) ⇒ ∠ CBF = (180° – x) ⇒ 130° = 180° – x [∵ ∠ CBF = 130 °] ⇒ x = (180° – 130° ) = 50° Hence, x = 50° (1 mark)

In the figure, sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively. If $∠ C B F = 130^{\circ} a n d ∠ C D E = x^{\circ},$ find the value of x.
(2 Marks)

ABCD is a cyclic quadrilateral.
We know that in a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
∴ ∠ CBF = ∠ CDA (1 mark)
⇒ ∠ CBF = (180° – x)
⇒ 130° = 180° – x [∵ ∠ CBF = 130 °]
⇒ x = (180° – 130° ) = 50°
Hence, x = 50° (1 mark)