The magnitude of the outer angle is 108 °, and the magnitude of the inner ones

| February 18, 2021 | education

The magnitude of the outer angle is 108 °, and the magnitude of the inner ones not adjacent to it is related as 5: 4. Find the smaller angle of the triangle.

First way.

Let the value of the angle ACB = 4 * X0, then the angle ABC = 5 * X0.

The external angle of a triangle is equal to the sum of two angles that are not adjacent to it.

Then the angle ВAD = ABC + AСB.

108 = 5 * X + 4 * X.

9 * X = 108.

X = 108/9 = 12.

Then the angle ACB = 4 * 12 = 480.

Angle ABC = 5 * 12 = 600.

Angle BAC = (180 – 48 – 60) = 720.

Second way.

The angles VAD and BAC are adjacent, then the angle BAC = (180 – 108) = 720.

Let the value of the angle ACB = 4 * X0, then the angle ABC = 5 * X0.

Then 72 + 4 * X + 5 * X = 180.

9 * X = 108.

X = 108/9 = 12.

Then the angle ACB = 4 * 12 = 480.

Angle ABC = 5 * 12 = 600.

Answer: The smallest angle of the triangle is 480.



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