Question

in ∆ABC , 3 angle A = angle B + angle C and angle B : angle C = 2:1, then find all angles of triangle. Which type of ∆ABC is ?

Answer 1

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HERE'S THE ANSWER..

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♠️ In ∆ ABC

⏺️A + B + C = 180° ( A.S.P )__( 1 )

✔️ Is is given that

=> 3 A = B + C ____ ( 2 )

⏺️ By putting value of ( B + C ) in ( 1 )

=> A + ( B + C ) = 180°

=> A + 3 A = 180°

=> 4 A = 180°

=> $\boxed{A \:=\:45°}$

✔️ It is given

=> B / C = 2 / 1

=> B = 2 C __( 3 )

⏺️ Now by Eqn ( 2 )

=> 3 A = B + C

=> 3 ( 45 ) = B + C

=> 135 = B + C

=> 2 C + C = 135 { from eqn ( 3 ) }

=> 3 C = 135

=> $\boxed{ C\:=\:45°}$

⏺️ Now by Eqn ( 1 )

=> A + B + C = 180°

=> 45° + 45° + B = 180°

=> B = 180° - 90°

=> $\boxed{ C\:=\:90°}$

✔️Now by computing ∆ ABC

▶️ We get the above image↑↑↑

=> If two angle are equal then their opp. sides will be equal and one angle is 90° , hence it will be a

=> $\boxed{ isosceles\: right \:angled \: triangle}$

HOPE HELPED...

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Answer 2

→A + B + C = 180 ( ASP )

→3A = B + C

from above eqn

A = 45.

B / C = 2 / 1

B = 2 C

C = 45

now

90 + C = 180

C = 90

it is isosceles right triangle