If one of the angles of an isosceles triangle is a) 58 * b) 20 * c) 80 *,

| April 5, 2021 | education

If one of the angles of an isosceles triangle is a) 58 * b) 20 * c) 80 *, then determine the degree measure of other angles. how many possible options there can be

Since, according to the condition of the problem, it is not indicated which angle of an isosceles triangle is given in conditions a), b), c), it is necessary to assume that the angle can be at the apex of an isosceles triangle or at the base. Thus, it is necessary to consider two options for the location of a given angle: the first is at the apex, the second is at the base.

We use these conditions a): the angle is 58 °. First option: the angle is at the apex of the isosceles triangle. Since the sum of the interior angles of any triangle is 180 °, then knowing one angle of -58 ° we determine the sum of the other two angles.

180 ° – 58 ° = 112 °.

In an isosceles triangle, the angles at the base are equal and each of them will be.

112 °: 2 = 61 °.

This means that for the first option the angles are equal.

58 °, 61 °, 61 °.

Second option: the angle is at the base of the isosceles triangle. In an isosceles triangle, the angles at the base are equal and each of them will be 58 °. Since the sum of the interior angles of any triangle is 180 °, knowing two angles (58 ° and 58 °), we determine the third angle.

180 ° – (58 ° + 58 °) = 180 ° – 116 ° = 64 °.

This means that for the second option the angles are equal.

58 °, 58 °, 64 °.

We use these conditions b): the angle is 20 °. First option: the angle is at the apex of the isosceles triangle. Since the sum of the interior angles of any triangle is 180 °, then knowing one angle -20 ° we determine the sum of the other two angles.

180 ° – 20 ° = 160 °.

Each angle at the base is equal to.

160 °: 2 = 80 °.

This means that for the first option the angles are equal.

20 °, 80 °, 80 °.

The second option is the 20 ° angle is at the base of the triangle. We carry out similar calculations as in a).

180 ° – (20 ° + 20 °) = 180 ° – 40 ° = 140 °.

This means that for the second option the angles are equal.

20 °, 20 °, 140 °.

We use these conditions c): the angle is 80 °. First option: the angle is at the apex of an isosceles triangle. Since the sum of the interior angles of any triangle is 180 °, then knowing one angle of 80 ° we determine the sum of the other two angles.

180 ° – 80 ° = 100 °.

This means that each angle at the base is equal to.

100 °: 2 = 50 °.

For the first option, the angles are equal.

80 °, 50 °, 50 °.

We carry out the values ​​of the angles similar to the above calculations of the second option.

180 ° – (80 ° + 80 °) = 180 ° – 160 ° = 20 °.

This means that for the second option the angles are equal.

20 °, 80 °, 80 °.

Answer. a) 58 °, 61 °, 61 °. 58 °, 58 °, 64 °.

b) 20 °, 80 °, 80 °. 20 °, 20 °, 140 °.

c) 80 °, 50 °, 50 °. 20 °, 80 °, 80 °.



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