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.

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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