ABCD is a rhombus. If ∠BAC = 38°, find : (i) ∠ACB (ii) ∠DAC (iii) ∠ADC.

Question

KnowledgeBoat · Accepted Answer

(i) In a rhombus, all sides are equal. ⇒ AB = BC = CD = DA And, opposite angles of a rhombus are equal. ∠BAC = ∠ACB It is given that ∠BAC = 38°. So, ∠ACB = ∠BAC = 38°. Hence, the value of ∠ACB is 38°. (ii) Since ABC is a triangle, the sum of angles in a triangle is 180°. Therefore, ⇒ ∠ABC \+ ∠BAC \+ ∠ACB = 180° ⇒ ∠ABC \+ 38° \+ 38° = 180° ⇒ ∠ABC \+ 76° = 180° ⇒ ∠ABC = 180° \- 76° ⇒ ∠ABC = 104° Since opposite angles of a rhombus are equal: ⇒ ∠ABC = ∠ADC ⇒ ∠ADC = 104° As AD = CD, we have: ∠DAC = ∠DCA Now, ⇒ ∠DAC = [180° - 104°] = [76°] = 38° Hence, the value of ∠DAC is 38°. (iii) Since opposite angles of a rhombus are equal: ⇒ ∠ABC = ∠ADC ⇒ ∠ADC = 104° Hence, the value of ∠ADC is 104°.

Mathematics

ABCD is a rhombus. If ∠BAC = 38°, find :
(i) ∠ACB
(ii) ∠DAC
(iii) ∠ADC.

Quadrilaterals

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Mathematics

ABCD is a rhombus. If ∠BAC = 38°, find :(i) ∠ACB(ii) ∠DAC(iii) ∠ADC.