Math, asked by ramkv4, 1 year ago

Find x in the traingle

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Answers

Answered by shivangihowlader29
0

Answer:

3)67°

Step-by-step explanation:

@ACB+123°=180°

@ACB=57°

@ACB+@ABC+@BAC=180°[sum of interior angles of a triangle=180°]

57°+x+56°=180°

x+113°=180°

x=67°

Answered by MaIeficent
25

Step-by-step explanation:

\mathbf\red{Given:-}

  • A triangle ABC in which:-

  • \angle \: A = 56\degree

  • Exterior \angle ACD = 123\degree

\mathbf\blue{To\:Find}

  • The value of \angle\: A = x\degree

\mathbf\green{Solution:-}

As,we know that:-

Exterior angle = Sum of interior opposite angles.

In \triangle\: ABC \\\\</p><p></p><p>\angle \: A + \angle \: B = Exterior\: angle \: ACD \\\\</p><p>\implies 56\degree + x\degree = 123\degree \\\\</p><p></p><p>\implies x\degree = 123\degree - 56\degree

\tt\purple{\implies \: x\degree = 67\degree}

____________

\mathbf\pink{Alternatively}

\angle \: ACD + \angle\: ACB = 180\degree [ Sim of angles on a straight line = 180°]

 123\degree+ \angle \: ACB = 180\:degree \\\\</p><p></p><p>\angle \: ACB = 180\degree- 123\degree \\\\</p><p></p><p>= 57\degree

In ∆ABC :-

\angle\: A+ \angle\: B + \angle\: ACB = 180° [ Sum of angles in a triangle = 180°]

 \implies 56\degree+ x\degree + 57\degree = 180\degree \\\\</p><p></p><p>\implies 113\degree+ x\degree = 180\degree \\\\</p><p></p><p>\implies x\degree = 180\degree- 113\degree}

\tt\purple{\implies x\degree = 67°}

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