Question

В ∆ABC , AB=BC , BD-медиана , угол CBD=35. Найдите угол ABC.

Answer 1

Ответ:

Изи

Пошаговое объяснение:

Т.к АВ=ВС, то треугольник АВС - равнобедренный

По свойству медианы в р/б треугольнике ВD-биссектриса угла АВС

По рисунку видно что угол АВС=угол АВD+угол CBD

А тк ВD-биссектриса угла АВС то угол АВD=угол CBD

угол АВС=35 градусов+35 градусов=70 градусов

Answer 2

To find the angle ABC in ∆ABC, we can use the properties of a median in an isosceles triangle.

Given:

• ∆ABC with AB = BC (isosceles triangle).
• BD is a median, which means it divides the side AC into two equal segments.

Let's proceed with the solution:

Step 1: Draw the triangle and median. We have an isosceles triangle ABC with BD as the median. The angles at points B and C are equal due to the isosceles property.

Step 2: Identify the information given. We know that ∠CBD = 35 degrees.

Step 3: Find the measure of ∠BCD. Since BD is the median, it divides AC into two equal parts. Therefore, ∠BCD = ∠CBD = 35 degrees.

Step 4: Find the measure of ∠ABC. In any triangle, the sum of the angles is 180 degrees. So, we can use this property to find ∠ABC:

∠ABC + ∠BCD + ∠CBA = 180 degrees

Since ∠BCD = 35 degrees, and ∠CBA and ∠ABC are equal (due to the isosceles property), we can rewrite the equation as:

∠ABC + 35 + ∠ABC = 180

Combine like terms:

2∠ABC + 35 = 180

Subtract 35 from both sides:

2∠ABC = 145

Now, divide by 2 to solve for ∠ABC:

∠ABC = 145 / 2

∠ABC = 72.5 degrees

So, the measure of ∠ABC is 72.5 degrees.