-. The exterior angles obtained on producing the base of a triangle
both ways are 104° and 136º. Find the angles of the triangle.
answer this
Answers
Answer :
44° , 60° , 76°
Note :
★ Linear pairs of angles : Two adjacent angles lying on the same straight line is called Linear pair of angles .
★ Sum of linear pair of angles is 180° .
★ Linear pair of angles are supplementary .
★ Angle sum property of a triangle : The sum of all the interior angles of a triangle is 180° .
Solution :
Let's us assume ;
• A ∆ABC with base BC .
• BC produced along DE .
• ∠ABD = 104° and ∠ACE = 136°.
Now ,
=> ∠ABD + ∠ABC = 180° { linear pair }
=> 104° + ∠ABC = 180°
=> ∠ABC = 180° - 104°
=> ∠ABC = 76°
Also ,
=> ∠ACE + ∠ACB = 180° { linear pair }
=> 136° + ∠ACB = 180°
=> ∠ACB = 180° - 136°
=> ∠ACB = 44°
Also ,
=> ∠ABC + ∠ACB + ∠BAC = 180°
{ angle sum property of ∆ }
=> 76° + 44° + ∠BAC = 180°
=> 120° + ∠BAC = 180°
=> ∠BAC = 180° - 120°
=> ∠BAC = 60°
Hence ,
44° , 60° , 76° are the angles of the triangle under consideration .
Answer:
Here's your answer........✌✌✌✌✌✌
Hope this helps you...sorry my writing is bad......
