Question

in triangle abc, b= 55 and c=65 then the measure of an exterior angle of triangle abc cannot be ​

Answer 1

Step-by-step explanation:

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Answer 2

Given  : ΔABC , ∠B  = 55°  and  ∠C = 65°  

To Find : the measure of an exterior angle of ΔABC cannot be ______

Solution:

Exterior angle of Triangle = Sum of opposite two internal angles

=> Exterior angle of ∠A  = ∠B + ∠C

=>  Exterior angle of ∠A  = 55° +  65°  

=>  Exterior angle of ∠A  = 120°

Exterior angle  of ∠B +  ∠B = 180°  ( Linear Pair )

=> Exterior angle  of ∠B +  55° = 180°

=> Exterior angle  of ∠B   = 125°

Exterior angle  of ∠C +  ∠C = 180°  ( Linear Pair )

=> Exterior angle  of ∠C + 65° = 180°

=> Exterior angle  of ∠C   = 115°

Hence Exterior angles are 115°  ,  120° , 125°

Any angles other than these angles can not be exterior angle of triangle ABC

Exterior angle of ΔABC  can not be  = (0° , 180°) - {115°  ,  120° , 125°}

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