In each of the following figures, find the value of x : (i) (ii) (iii)

Question

KnowledgeBoat · Accepted Answer

(i) From figure, ∠A = 40° In △ABC, AB = AC ⇒ ∠C = ∠B = z (let) (Angles opposite to equal sides are equal) By angle sum property of triangle, ⇒ ∠A + ∠B + ∠C = 180° ⇒ 40° + z + z = 180° ⇒ 2z = 180° - 40° ⇒ 2z = 140° ⇒ z = ⇒ z = 70° ⇒ ∠C = ∠B = 70°. From figure, ⇒ ∠C + ∠ACD = 180° (Linear pair) ⇒ 70° + x° = 180° ⇒ x° = 180° - 70° ⇒ x° = 110° ⇒ x = 110. Hence, the value of x = 110. (ii) From figure, In △CAD, ⇒ AC = CD ⇒ ∠CDA = ∠CAD = 30° (Angles opposite to equal sides are equal) In △ABD, By angle sum property of triangle, ⇒ ∠DBA + ∠BAD + ∠BDA = 180° ⇒ x° + ∠BAC + ∠CAD + ∠BDA = 180° ⇒ x° + 65° + 30° + 30° = 180° ⇒ x° + 125° = 180° ⇒ x° = 180° - 125° ⇒ x° = 55° ⇒ x = 55. Hence, the value of x = 55. (iii) In △ABC, AB = AC ⇒ ∠ABC = ∠ACB = 55° (Angles opposite to equal sides in a triangle are equal) In △ABD, By angle sum property of triangle, ⇒ ∠ABD + ∠BDA + ∠BAD = 180° ⇒ 55° + 75° + ∠BAD = 180° ⇒ 130° + ∠BAD = 180° ⇒ ∠BAD = 180° - 130° ⇒ ∠BAD = 50°. In △ABC, By angle sum property of triangle, ⇒ ∠ABC + ∠ACB + ∠BAC = 180° ⇒ 55° + 55° + ∠BAD + ∠CAD = 180° ⇒ 55° + 55° + 50° + x° = 180° ⇒ 160° + x° = 180° ⇒ x° = 180° - 160° ⇒ x° = 20° ⇒ x = 20. Hence, value of x = 20.

Mathematics

In each of the following figures, find the value of x :
(i)
(ii)
(iii)

Triangles

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