In the given figure, x : y = 2 : 3 and ∠ACD = 120°. Find the values of x,y and z.

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Solution

$\begin{array}{l} Let x = 2 k and y=3 k \\ ∴ 2 k + 3 k = 120^{0} (e xterior angle property) \\ = > 5 k = 120^{0} \\ = > k = 24^{0} \\ ∴ x = 2 \times 24^{0} = 48^{0} and y=3 \times 24^{0} = 72^{0} \\ In Δ ABC: \\ ∠ A + ∠ B + ∠ C = 180^{0} \\ = > 48^{0} + 72^{0} + ∠ {C=180}^{0} \\ => ∠ C = 180^{0} - 120^{0} \\ => ∠ C = 60^{0} \\ ∴ z = 60^{0} \end{array}$

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In the given figure, x : y = 2 : 3 and ∠ACD = 120°. Find the values of x,y and z.

Let x=2k and y=3k∴2k+3k=1200 (exterior angle property)=>5k=1200=>k=240∴x=2×240=480 and y=3×240=720In ΔABC: ∠A+∠B+∠C=1800 =>480+720+∠C=1800 =>∠C=1800−1200 =>∠C=600 ∴ z=600