Question

Suppose that α and β are the angles of a triangle. It is known that: 58°≤α≤59° and 102°≤β≤103°. Find the possible values of the third angle.

Answer 1

The possible values of the third angle are from 18° to 20°

Step-by-step explanation:

The sum of the measures of the angles in any triangle is 180°

The given is:

1. α and β are two angles of a triangle

2. 58° ≤ α ≤ 59°

3. 102° ≤ β ≤ 103°

Assume that the third angle is Ф

∵ α + β + Ф = 180°

- Subtract α + β from both sides

∴ Ф = 180 - (α + β) ⇒ (1)

∵ 58° ≤ α ≤ 59°

∵ 102° ≤ β ≤ 103°

- Add the two inequalities

∴ 160° ≤ α + β ≤ 162°

- By substituting α + B = 160 in equation 1

∴ Ф = 180 - 160

∴ Ф = 20°

- By substituting α + B = 162 in equation 1

∴ Ф = 180 - 162

∴ Ф = 18°

- Put Ф in the form of inequality

∴ 18° ≤ Ф ≤ 20°

The possible values of the third angle are from 18° to 20°

Learn more:

You can learn more about triangle in brainly.com/question/3617539

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