Question

Кут при вершині рівнобедреного трикутника дорівнює 40° знайти кут між основою та бісектрисою проведеною до бічної сторони​

Answer 1

Вот надеюсь я тебе помогла

Answer 2

Finding the Angle between the Base and the Bisector of an Isosceles Triangle

To find the angle between the base and the bisector of an isosceles triangle, we need to use the properties of isosceles triangles and the angle bisector theorem.

An isosceles triangle has two equal sides and two equal angles. In this case, we are given that the angle at the vertex of the triangle is 40°. Let's denote this angle as A.

According to the angle bisector theorem, the angle bisector of an angle in a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Let's denote the angle between the base and the bisector as B. We can use the angle bisector theorem to find the relationship between B and A.

The angle bisector theorem states that the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the sides opposite those segments.

In this case, the angle bisector divides the base into two segments. Let's denote the lengths of these segments as x and y. The lengths of the equal sides of the triangle can be denoted as c.

According to the angle bisector theorem, we have the following relationship:

x/y = c/c

Since the triangle is isosceles, the lengths of the equal sides are the same. Therefore, we can simplify the equation to:

x/y = 1

Now, let's consider the angles formed by the segments x and y with the base. The angle formed by segment x is B, and the angle formed by segment y is A - B.

Using the properties of triangles, we know that the sum of the angles in a triangle is 180°. Therefore, we can write the following equation:

B + (A - B) + 40 = 180

Simplifying the equation, we get:

A + 40 = 180

Substituting the value of A (40°), we can solve for B:

40 + 40 = 180

80 = 180

B = 180 - 80

B = 100°

Therefore, the angle between the base and the bisector of the isosceles triangle is 100°.

Please note that the sources provided did not contain specific information about this particular problem. The solution was derived using the properties of isosceles triangles and the angle bisector theorem.