In an isosceles triangle, the two angles are 4: 5. Find all corners.

| September 1, 2021 | education

The problem has two solutions.

Since the triangle ABC is isosceles with the base of the AC, then the angle BAC = BCA.

Let the angle BCA = BAC = 5 * X0, then the angle ABC = 4 * X0.

The sum of the interior angles of a triangle is 180, then:

4 * X + 5 * X + 5 * X = 180.

14 * X = 180.

X = 180/14 = 90/7.

Then the angle BCA = BAC = 5 * 90/7 = 450/7 = 64 (2/7) 0.

Angle ABC = 4 * 90/7 = 360/7 = 51 (3/7) 0.

Let the angle BCA = BAC = 4 * X0, then the angle ABC = 5 * X0.

The sum of the interior angles of the triangle is 1800, then:

4 * X + 4 * X + 5 * X = 180.

13 * X = 180.

X = 180/13.

Then the angle BCA = BAC = 4 * 180/13 = 720/13 = 55 (5/13) 0.

Angle ABC = 5 * 180/13 = 900/13 = 69 (3/13) 0.

Answer: The angles of a triangle are 64 (2/7) 0, 51 (3/7) 0 or 55 (5/13) 0, 69 (3/13) 0.



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