Calculate x : (i) (ii)

Question

Calculate x : (i)  (ii)

KnowledgeBoat · Accepted Answer

(i) In △ ABC, ⇒ BC = AC (Given) ∴ ∠BAC = ∠CBA = 37° (Angles opposite to equal sides are equal) By angle sum property of triangle, ⇒ ∠BAC + ∠CBA + ∠ACB = 180° ⇒ 37° + 37° + ∠ACB = 180° ⇒ ∠ACB + 74° = 180° ⇒ ∠ACB = 180° - 74° = 106°. From figure, Since, BCD is a straight line, ∴ ∠ACB + ∠ACD = 180° ⇒ 106° + ∠ACD = 180° ⇒ ∠ACD = 180° - 106° = 74°. In △ ACD, ⇒ CD = AD (Given) ∴ ∠CAD = ∠ACD = 74° (Angles opposite to equal sides are equal) By angle sum property of triangle, ⇒ ∠CAD + ∠ACD + ∠ADC = 180° ⇒ 74° + 74° + x = 180° ⇒ 148° + x = 180° ⇒ x = 180° - 148° = 32°. Hence, x = 32°. (ii) In △ ABC, ⇒ BC = AC (Given) ∴ ∠BAC = ∠CBA = 50° (Angles opposite to equal sides are equal) By angle sum property of triangle, ⇒ ∠BAC + ∠CBA + ∠ACB = 180° ⇒ 50° + 50° + ∠ACB = 180° ⇒ ∠ACB + 100° = 180° ⇒ ∠ACB = 180° - 100° = 80°. From figure, Since, BCD is a straight line, ∴ ∠ACB + ∠ACD = 180° ⇒ 80° + ∠ACD = 180° ⇒ ∠ACD = 180° - 80° = 100°. In △ ACD, ⇒ CD = AC (Given) ∴ ∠CAD = ∠ADC = x (Angles opposite to equal sides are equal) By angle sum property of triangle, ⇒ ∠CAD + ∠ACD + ∠ADC = 180° ⇒ x + x + 100° = 180° ⇒ 2x + 100° = 180° ⇒ 2x = 180° - 100° ⇒ 2x = 80° ⇒ x = = 40°. Hence, x = 40°.

Mathematics

Calculate x :
(i)
(ii)

Triangles

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Calculate x :(i)(ii)