Question

INA TRIANGLE ABC ,IF ANGLE A =120 DEGREE AND AB =AC .FIND ANGLE B AND ANGLE C

Answer 1

$\bigstar$ Question:

• In a triangle ABC, if $\angle$A = 120°, and AB = AC, then find $\angle$B and $\angle$C.

$\bigstar$ Given:

• $\angle$A = 120°
• AB = AC

$\bigstar$To find:

• $\angle$B
• $\angle$C

$\bigstar$ Solution:

$\because$AB = BC in $\triangle$ABC,

$\therefore$ $\angle$ ABC = $\angle$ BCA

( Angles opposite to equal sides of a triangle are equal )

Now in $\triangle$ABC,

$\angle$BAC + $\angle$ABC + $\angle$ACB = 180°

(Angle Sum Property Of A Triangle)

$\implies$ 120° + $\angle$ABC + $\angle$ABC = 180°

( $\because$ $\angle$ABC = $\angle$ ACB)

$\implies$ 2 $\angle$ABC = 180° - 120°

$\implies$ 2 $\angle$ABC = 60°

$\implies$ $\angle$ABC = $\frac{60°}{2}$

$\implies$ $\boxed{\rm\angle\:ABC\: =\: 30°}$

$\therefore$ $\angle$B = 30° and $\angle$C = 30°.

$\bigstar$Answers:

Therefore,

• $\rm\boxed{\angle\:B = 30°\:}$
• $\rm\boxed{\angle\:C\: =\: 30°\:}$

Answer 2

Step-by-step explanation:

Hope this will help you