Q1 of 34 Page 116

The exterior angles obtained on producing the base of a triangle both ways are 104° and 136°. Find the angles of the triangle.


Given: exterior angles: ∠ ABD = 104° and ∠ ACE = 136°


As D, B and C all lie on the same line.


So,


∠ ABD + ∠ ABC = 180°


⇒ 104° + ∠ ABC = 180°


⇒ ∠ ABC = 180° - 104°


⇒ ∠ ABC = 76°


Similarly, As E, B and C all lie on the same line.


So,


∠ ACB + ∠ ACE = 180°


⇒ ∠ ACB + 136° = 180°


⇒ ∠ ACB = 180° - 136°


⇒ ∠ ACB = 44°


As we know, using theorem (1), in any triangle, sum of the three interior angles is 180°.


So,


∠ABC+ ∠ACB + ∠CAB = 180°


⇒ 76° + 44° + ∠ CAB = 180°


⇒ ∠ CAB = 180° - 76° - 44°


⇒ ∠ CAB = 60°


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