Question

find the value of x and explain it

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Answer 1

Answer:

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Answer 2

Answer:

x = 70°

Step-by-step explanation:

From fig.,  ABCD is a quadrilateral.

In fig., consider Δ BCD

∠CBD + ∠BDC + ∠C =180° .........(angle sum property of a Δ)

30° + 10° + ∠C = 180°

∴ ∠C = 140 °

AB ≅ AD

∴ ∠ ADB = ∠ ABD = x .........(angle opposite congruent side)

Quadrilateral ABCD must be a cyclic quadrilateral so as to find the value of x.

∴ ∠A +∠C = 180° ........(opposites angles of Quadrilateral are supplementary)

∴ ∠A + 140° = 180°

∴ ∠A = 40°

Similarly, ∠B + ∠D =180°

(x+30°) + (∠ADB + 10°) = 180°

∴ (x+30°) + (x+10°) =180° ..........(∠ABD ≅ ∠ADB)

∴ x = 70°