Question

Розв'яжіть задачі будь ласка. 1) одна сторона трикутника дорівнює 8см. Дві інші сторони відносяться як 3:5 а їх різниця дорівнює 6см. Знайти периметр трикутника. 2) два зовнішні кути трикутника дорівнюють 125 і 135. Знайти внутрішній кут трикутника, не суміжний з даними

Answer 1

Ответ:1- 20см 2- 15°

Пошаговое объяснение:

Answer 2

Problem 1: Finding the perimeter of a triangle

To find the perimeter of a triangle, we need to know the lengths of all three sides. In this problem, we are given that one side of the triangle is 8 cm, and the other two sides are in a ratio of 3:5. The difference between these two sides is 6 cm.

Let's solve this problem step by step:

Step 1: Let's assume the lengths of the other two sides are 3x and 5x, where x is a common factor.

Step 2: We are given that the difference between these two sides is 6 cm. So, we can set up the equation: 5x - 3x = 6.

Step 3: Solving the equation, we find that 2x = 6, which implies x = 3.

Step 4: Now, we can find the lengths of the other two sides: 3x = 3 * 3 = 9 cm and 5x = 5 * 3 = 15 cm.

Step 5: Finally, we can calculate the perimeter of the triangle by adding the lengths of all three sides: 8 cm + 9 cm + 15 cm = 32 cm.

Therefore, the perimeter of the triangle is 32 cm.

Problem 2: Finding the interior angle of a triangle

In this problem, we are given the measures of two exterior angles of a triangle, which are 125 degrees and 135 degrees. We need to find the measure of the interior angle that is not adjacent to these given angles.

To find the measure of the interior angle, we can use the fact that the sum of the measures of the interior angles of a triangle is always 180 degrees.

Let's solve this problem step by step:

Step 1: We know that the sum of the measures of the exterior angles of a triangle is always 360 degrees. So, we can find the measure of the third exterior angle by subtracting the sum of the given exterior angles from 360 degrees: 360 degrees - (125 degrees + 135 degrees) = 100 degrees.

Step 2: The interior angle that is not adjacent to the given angles is the supplementary angle of the third exterior angle. So, we can find its measure by subtracting the measure of the third exterior angle from 180 degrees: 180 degrees - 100 degrees = 80 degrees.

Therefore, the measure of the interior angle that is not adjacent to the given angles is 80 degrees.