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In Fig., AB divides ∠DAC in the ratio 1: 3 and AB =DB. Determine the value of x. |
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Answer» Given, AB divides ∠DAC in the ratio 1: 3 ∠DAB: ∠BAC = 1: 3 ∠DAC + ∠EAC = 180° ∠DAC + 108° = 180° ∠DAC = 180° – 108° = 72° ∠DAB = \(\frac{1}{4}\) x 72° = 18° ∠BAC = \(\frac{3}{4}\) x 72° = 54° In ΔADB ∠DAB + ∠ADB + ∠ABD = 180° 18° + 18° + ∠ABD = 180° 36° + ∠ABD = 180° ∠ABD = 180° – 36° = 144° ∠ABD + ∠ABC = 180°(Linear pair) 144° + ∠ABC = 180° ∠ABC = 180° – 144° = 36° In ΔABC ∠BAC + ∠ABC + ∠ACB = 180° 54° + 36° + x = 180° 90° + x = 180° x = 180° – 90° = 90° Thus, x = 90° |
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