Six numbers, which are the degree measures of the three inner and three outer corners of an acute-angled

| September 15, 2021 | education

Six numbers, which are the degree measures of the three inner and three outer corners of an acute-angled triangle, have the property that if you write them in ascending order, then each next number will be the same amount more than the previous one. Find the degree measure of the smallest inner angle of this triangle.

The sum of the interior angles of a triangle is 180.

The sum of the outer angles of a triangle is 360.

Let the smallest internal angle be equal to X0, and the difference between adjacent angles in ascending order is equal to Y0.

Then the sum of the interior angles will be equal to: X + (X + Y) + (X + 2 * Y) = 180.

3 * X + 3 * Y = 180.

X + Y = 60.

Y = 60 – X. (1).

The sum of the inner and outer corners will be:

X + (X + Y) + (X + 2 * Y) + (X + 3 * Y) + (X + 4 * Y) + (X + 5 * Y) = 540.

6 * X + 15 * Y = 540.

Substitute equation (1).

6 * X + 15 * (60 – X) = 54.

9 * X = 900 – 540 = 36.

X = 360/9 = 40.

Answer: The smallest internal angle is 40.



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