Q7 of 28 Page 95

Find x°, y°, z° from the figure, where AB = BD, BC = DC and ∠DAC 30o.

Theorem 1: Sum of all the angles in the triangle is 180°.


In Δ ABD,


We know that, AB = BD


∴ ∠ A = ∠ D


⇒ 30° = x°


Hence, ∠ A + ∠ B + ∠ C = 180°


⇒ 30° + ∠ B + 30° = 180°


⇒ ∠ B + 60° = 180°


⇒ ∠ B = 180° - 60°


⇒ ∠ B = 120°


∠ DBA + ∠ DBC = 180° (Sum of adjacent angles is 180°)


⇒ 120° + y° = 180°


⇒ y° = 180° - 120°


⇒ y° = 60°


In Δ DBC


We know that, BC = DC


∴ ∠ B = ∠ D


⇒ y° = z°


⇒ 60° = z°


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