The 2 angles of the triangle are 50 and 70 degrees. Find the angle between the bisectors of these angles.
May 22, 2021 | education
| Let’s call the triangle ABC, in which the angle A = 50 °, the angle B = 70 °. The bisectors AH and BE pass through the corners A and B, intersecting at point K. The triangle AKB is obtained. It is necessary to find the angle of the AKB.
A bisector is a ray that bisects an angle, so:
CАH = HAB = 1/2 A;
CAH = HAB = 1/2 50 °;
CAH = HAB = 25 °;
ABE = EBC = 1/2 B;
ABE = EBC = 1/2 70 °;
ABE = EBC = 35 °;
The sum of the angles in a triangle is always 180 °, knowing the angles HAB and ABE of the triangle AKB, we find the angle AKB:
AKB = 180 ° – 25 ° – 35 °;
AKB = 120 ° – the angle between the bisectors.
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