Q. 14.5( 22 Votes )

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

Answer :


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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Karnataka Board - Mathematics Part I