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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