Question

Один із зовнішніх кутів трикутника дорівнює 132°,а один із внутрішніх кутів,не суміжних з ним,у три рази більший від іншого. Знайдіть внутрішні кути його трикутника

Answer 1

Ответ: 48⁰      33⁰      99⁰

Объяснение: Див. додаток

Answer 2

Problem Analysis

We are given that one of the external angles of a triangle is 132°, and one of the non-adjacent internal angles is three times larger than the other. We need to find the measures of the internal angles of the triangle.

Solution

Let's assume the three internal angles of the triangle are A, B, and C, with A being the angle opposite to the external angle of 132°.

We know that the sum of the internal angles of a triangle is always 180°. Therefore, we can write the equation:

A + B + C = 180°

We are also given that one of the non-adjacent internal angles (let's assume it is B) is three times larger than the other internal angle (let's assume it is C). So we can write the equation:

B = 3C

Substituting the value of B in terms of C into the first equation, we get:

A + 3C + C = 180°

Simplifying the equation, we have:

A + 4C = 180°

Now, we need to find the values of A and C.

To find the value of C, we can solve the equation:

4C = 180° - A

Dividing both sides of the equation by 4, we get:

C = (180° - A) / 4

Since B is three times larger than C, we can write:

B = 3C = 3[(180° - A) / 4]

Finally, we can substitute the values of A, B, and C into the equation A + B + C = 180° to find the values of the angles.

Let's calculate the values of A, B, and C using the given information.

Calculation

Given: One of the external angles = 132°

We can calculate the values of A, B, and C using the equations derived above.

A = 132°

C = (180° - A) / 4 = (180° - 132°) / 4 = 48° / 4 = 12°

B = 3C = 3 * 12° = 36°

Therefore, the internal angles of the triangle are A = 132°, B = 36°, and C = 12°.

Answer

The internal angles of the triangle are: - Angle A = 132° - Angle B = 36° - Angle C = 12°

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