Question

Find x in the traingle

Answer 1

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°

Answer 2

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°]

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

$\tt\purple{\implies x\degree = 67°}$