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An exterior angle of a triangle …

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An exterior angle of a triangle is 115°& one of the interior opposite angle is 35°. Find the other two angles.

Posted by Hariom Dalal 6 years, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Sia ? 6 years, 5 months ago

Let in {tex}\bigtriangleup{/tex}ABC, exterior {tex}\angle{/tex}ACE = 115^o and {tex}\angle{/tex}A = 35^o
We know that,
{tex}\angle{/tex}ACE = {tex}\angle{/tex}A + {tex}\angle{/tex}B (Exterior Angle Theorem)
{tex}\Rightarrow{/tex} 115^o = 35^o + {tex}\angle{/tex}B
{tex}\angle{/tex}B = 115^o – 35^o = 80^o
Again, in {tex}\bigtriangleup{/tex}ABC,
{tex}\angle{/tex}A + {tex}\angle{/tex}B + {tex}\angle{/tex}C = 180^o
(The sum of the three angles of a triangle is 180^o)
{tex}\Rightarrow{/tex} 35^o + 80^o + {tex}\angle{/tex}C = 180^o
{tex}\Rightarrow{/tex} 115^o + {tex}\angle{/tex}C = 180^o
{tex}\Rightarrow{/tex} {tex}\angle{/tex}C = 180^o – 115^o = 65^o

Srishtika Murugan 6 years, 5 months ago

In the figure, By linear pair axiom, Angle ACB = 180 - 115 =65 By angle sum property, Angle ABC=180-(AngleBAC +AngleACB)=180-(35+65)=180-100=80

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