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Find the interior angle BCA.

Mathematics

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Answer

∠ABC=70∘\angle ABC = 70^\circ

Step-by-step solution

3 steps
  1. Find the interior angle ∠BCA\angle BCA.

    Angles on a straight line sum to 180∘180^\circ.

    ∠BCA+125∘=180∘\angle BCA + 125^\circ = 180^\circ ∠BCA=180∘−125∘\angle BCA = 180^\circ - 125^\circ ∠BCA=55∘\angle BCA = 55^\circ
  2. Identify the type of triangle and its properties.

    The markings on sides AB and BC indicate that AB=BCAB = BC. Therefore, △ABC\triangle ABC is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal.

    ∠BAC=∠BCA\angle BAC = \angle BCA ∠BAC=55∘\angle BAC = 55^\circ
  3. Find the size of angle ABC using the sum of angles in a triangle.

    The sum of angles in a triangle is 180∘180^\circ.

    ∠ABC+∠BAC+∠BCA=180∘\angle ABC + \angle BAC + \angle BCA = 180^\circ ∠ABC+55∘+55∘=180∘\angle ABC + 55^\circ + 55^\circ = 180^\circ ∠ABC+110∘=180∘\angle ABC + 110^\circ = 180^\circ ∠ABC=180∘−110∘\angle ABC = 180^\circ - 110^\circ ∠ABC=70∘\angle ABC = 70^\circ
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