The outer angle of a triangle is 4 times one of its non-adjacent angles, and the other non-adjacent

| July 13, 2021 | education

The outer angle of a triangle is 4 times one of its non-adjacent angles, and the other non-adjacent angle is 84 °. Find an adjacent corner.

From the condition, we know that the outer angle of the triangle is 4 times greater than one of the angles not adjacent to it, and the other non-adjacent angle is 84 °. In order to find the adjacent angle, compose and solve a linear equation.

Let us denote by the variable x one of the angles not adjacent to it, then the outer angle can be written as 4x.

We know that the outer angle is equal to the sum of two inner angles of a triangle that are not adjacent to it.

4x = x + 84;

4x – x = 84;

3x = 84;

x = 84: 3;

x = 28 °.

Then the outer angle is 4 * 28 = 112 °.

The sum of the adjacent angles of a triangle is 180 °.

180 ° – 112 ° = 68 °.



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