The bisector of the outer angle of an isosceles triangle ABC at the base AC forms an angle of 66 degrees
| August 8, 2021 | education
The bisector of the outer angle of an isosceles triangle ABC at the base AC forms an angle of 66 degrees with the straight line AC. Find (in degrees) the angle ABC.
Since AD is the bisector of the outer angle CAE, then the angle AED = CAD = 66, therefore, the value of the angle CAE = 2 * CAD = 2 * 66 = 132.
The angles CAB and SAE are interchangeable angles, the sum of which is 180, then the angle CAB = (180 – SAE) = (180 – 132) = 48.
Since the triangle ABC is isosceles with the base of the AC, then the angle ACB = CAB = 48, then the angle ABC = (180 – 48 – 48) = 84
Answer: The angle ABC is 84.
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