Question

Известно что сумма углов треугольника равна 180 градусов найдите градусную меру угла при основании равнобедренного треугольника,если известно,что он в 3 раза меньше угла при вершине!

Answer 1

Пусть угол при  при основании  будет Х,тогда угол при вершине будет 3Х ( а так,как два угла при основании у равнобедренного треугольника равны,то второй угол при основании тоже Х)
имея все это , составим уравнение
Х+ Х+ 3Х = 180 
5Х=180
Х=36 
значит угол у основания 36 градусов( второй тоже 36)
(угол при вершине 108 и два угла при основании по 36градусов= в сумме 180)

Answer 2

Finding the Degree Measure of the Base Angle of an Isosceles Triangle

To find the degree measure of the base angle of an isosceles triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Let's denote the degree measure of the base angle as x and the degree measure of the vertex angle as y.

According to the given information, the base angle is three times smaller than the vertex angle. Mathematically, we can express this relationship as:

x = (1/3)y

Since we know that the sum of the angles in a triangle is 180 degrees, we can write the equation:

x + x + y = 180

Substituting the value of x from the first equation into the second equation, we get:

(1/3)y + (1/3)y + y = 180

Simplifying the equation, we have:

(7/3)y = 180

To find the value of y, we can solve this equation. Multiplying both sides of the equation by (3/7), we get:

y = (180 * 3) / 7

Evaluating this expression, we find:

y ≈ 77.14 degrees

Now, we can substitute the value of y back into the first equation to find the value of x:

x = (1/3) * 77.14

Evaluating this expression, we find:

x ≈ 25.71 degrees

Therefore, the degree measure of the base angle of the isosceles triangle is approximately 25.71 degrees.

Conclusion

The degree measure of the base angle of an isosceles triangle, given that it is three times smaller than the vertex angle, is approximately 25.71 degrees.