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Q8. In the adjoining figure, ABCD is a rhombus in which ∠BAC = 40°. Find the measures of : (i) ∠ACB (ii) ∠ABC (iii) ∠ADC (iv) ∠ACD (v) ∠CAD |
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Answer» ∆ABC, AB = BC∴ ∠ACB = ∠BAC⇒ ∠ACB = 40°(ii) In ∆ABC,∠ACB + ∠BAC + ∠ABC = 180° (TOTAL sum of ANGLES of a TRIANGLE)⇒ 40° + 40° + ∠ABC = 180°⇒ 80° + ∠ABC = 180°⇒ ∠ABC = 180° - 80°⇒ ∠ABC = 100°(iii) ∠ADC = ∠ABC (opposite angles are EQUAL)⇒ ∠ADC = 100°(iv) DC ∥ AB and AC is the transversal,∴ ∠ACD = ∠CAB (alternate angles)⇒ ∠ACD = 40°(v) In ∆ADC, AD = DC∴ ∠CAD = ∠ACD⇒ ∠CAD = 40° |
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