Calculate the value of x in each of the following figure.
(i).
(ii)
(iii)
(iv)
(v)
(vi)
(i) 50°
Given, ∠BAE = 110° and ∠ACD = 120°
∠ACB + ∠ACD = 180° [Because BD is a straight line]
⇒ ∠ACB + 120° = 180°
⇒ ∠ACB = 60°_______________ (i)
In triangle ABC,
∠BAE = ∠ABC + ∠ACB
⇒ 110° = x + 60°
⇒ x = 50°
(ii) 120°
In triangle ABC,
∠A + ∠B + ∠C = 180° [Sum of angles of triangle ABC]
⇒ 30° + 40° + ∠C = 180°
⇒ ∠C = 110°
∠BCA + ∠DCA = 180° [Because BD is a straight line]
⇒ 110° + ∠DCA = 180°
⇒ ∠DCA = 70°_________________ (i)
In triangle ECD,
∠AED = ∠ECD + ∠EDC
⇒ x = 70°+ 50°
⇒ x = 120°
(iii) 55°
Explanation:
∠BAC = ∠EAF = 60°[Opposite angles]
In triangle ABC,
∠ABC + ∠BAC = ∠ACD
⇒ X°+ 60°= 115°
⇒ X°= 55°
(iv) 75°
Given AB||CD
Therefore,
∠BAD = ∠EDC = 60°[Alternate angles]
In triangle CED,
∠C + ∠D + ∠E = 180°[Sum of angles of triangle]
⇒ 45° + 60° + x = 180°[∠EDC = 60°]
⇒ x = 75°
(v) 30°
Explanation:
In triangle ABC,
∠BAC + ∠BCA + ∠ABC = 180°[Sum of angles of triangle]
⇒ 40° + 90° + ∠ABC = 180°
⇒ ∠ABC = 50°________________ (i)
In triangle BDE,
∠BDE + ∠BED + ∠EBD = 180°[Sum of angles of triangle]
⇒ x° + 100° + 50° = 180°[∠EBD = ∠ABC = 50°]
⇒ x° = 30°
(vi) x=30
Explanation:
In triangle ABE,
∠BAE + ∠BEA + ∠ABE = 180°[Sum of angles of triangle]
⇒ 75° + ∠BEA + 65° = 180°
⇒ ∠BEA = 40°
∠BEA = ∠CED = 40°[Opposite angles]
In triangle CDE,
∠CDE + ∠CED + ∠ECD = 180°[Sum of angles of triangle]
⇒ x° + 40° + 110° = 180°
⇒ x° = 30°