Respuesta :

Since this is a quadrilateral (4-sided polygon). The sum of interior angles has to be equal to 360.

Let x be the missing angle:

[tex]x + 105 + 113 + 75 = 360[/tex]

[tex]x + 293 = 360[/tex]

[tex]x = 360 - 293[/tex]

[tex]x = 67[/tex]

As we know that, for any shape with sides n, the sum of all it's interior angles is (n - 2) × 180°, so as the Shape ABCD is a quadrilateral with 4 sides, so sum of it's all interior angles is just going to be (4 - 2) × 180° = 2 × 180° = 360°, so if we assume the missing angle be [tex]\bf \angle A[/tex], by using the sum property we will be having ;

[tex]{:\implies \quad \sf \angle A+105{\degree}+113{\degree}+75{\degree}=360{\degree}}[/tex]

[tex]{:\implies \quad \sf \angle A+293{\degree}=360{\degree}}[/tex]

[tex]{:\implies \quad \sf \angle A=360{\degree}-293{\degree}}[/tex]

[tex]{:\implies \quad \boxed{\bf{\angle A=67{\degree}}}}[/tex]

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