Question

If angle ACD=114 degree and angle ABC =1/2of angle BAC. Find the value of angle ABC

Answer 1

$\huge\underline \orange{GIVEN}$

$➸{The\:side\:BC\:of \: \triangle ABC\:is\:produced\:to\:D}$

$➸\: \angle \: ACD\:=\:114^o$

$➸\: \angle\:ABC\:= \frac{1}{2} \angle \: BAC$

$\huge \green{❑ \: To\:find\:the\:value\:of \: \angle \: BAC}$

$\huge\pink{SOLUTION}$

$Let\: \angle\:ABC\:be\:x\:and\: \angle\:BAC\:be\:2x$

$\mathcal\red{ACCORDING\: \: TO\:THE\: EXTERIOR\:ANGLE\: PROPERTY}$

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

$♛\: \angle\:BAC\: + \angle\:ABC\: = \angle\:ACD$

$\implies\:2x + \: x \: = \: {114}^{o}$

$\implies\:3x \: = \: {114}^{0}$

$\implies\:x = \cancel{ \frac{114}{3}}$

$\implies\:x \: = {38}^{o}$

$\therefore\: \angle\:ABC\: = x = {38}^{o}$

$\therefore\: \angle\:BAC\:=2x\:=38\: \times 2 = 76$