Question

Найдите меньший угол равнобедренной трапеции, если два её угла относятся как 1:17. Ответ дайте в градусах.

Answer 1

Обозначим через "x", тогда
<A=x;
<B=17x;
Вспомним, что сумма односторонних углов равна 180, отсюда:
x+17x=180
18x=180
x=10(<A), тогда <B=180-10=170.
Наименьший угол 10.
Ответ : 10

Answer 2

Finding the Smaller Angle of an Isosceles Trapezoid

To find the smaller angle of an isosceles trapezoid when two of its angles are in the ratio 1:17, we can use the fact that the sum of the interior angles of any quadrilateral is always 360 degrees. Let's denote the two angles as x and 17x. Then we can set up an equation to solve for the value of x.

Step 1: Set up the equation based on the given ratio of the angles. Step 2: Solve for the value of x. Step 3: Calculate the smaller angle using the value of x.

Let's proceed with the calculations.

Step 1: Setting Up the Equation

The sum of the interior angles of a quadrilateral is 360 degrees. Therefore, we can write the equation: x + 17x + x + 17x = 360

Step 2: Solving for x

Combining like terms, we get: 36x = 360 Solving for x: x = 360 / 36 x = 10

Step 3: Calculating the Smaller Angle

Now that we have the value of x, we can calculate the smaller angle: Smaller angle = x = 10 degrees

So, the smaller angle of the isosceles trapezoid is 10 degrees.