Question

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​

Answer 1

(i) In ∆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°