# In an isosceles triangle ABC, the angle of the BCA is 70 degrees. what is the angle ABC and angle BAC equal?

September 14, 2021 | education

| Given:

Triangle ABC is isosceles.

Angle BCA = 70 °.

Find:

∠ ABC, ∠ BCA.

The ABC triangle is isosceles (according to the problem statement). Consequently, the angles at the base AC, by the property of an isosceles triangle, will be equal. Thus,

∠ BCA = ∠ BAC = 70 °. (by the property of isosceles triangular).

∠ BCA + ∠ BAC + ∠ ABC = 180 °. (by the theorem on the sum of the angles of a triangle).

2 * ∠ BCA + ∠ ABC = 180 °.

2 * 70 ° + ∠ ABC = 180 °.

∠ ABC = 180 ° – 140 °.

∠ ABC = 40 °.

Answer: the BAC angle is 70 °, the BAC angle is 70 °.

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