Question

У прямокутній трапеції тупий кут у 3 рази більший за гострий знайти кути трапеції

Answer 1

Finding the angles of a trapezoid with a larger obtuse angle

To find the angles of a trapezoid when the obtuse angle is three times larger than the acute angle, we can use the properties of the trapezoid.

Let's denote the acute angle as x. According to the given information, the obtuse angle is three times larger than the acute angle, so the obtuse angle can be represented as 3x.

In a trapezoid, the sum of the interior angles is always equal to 360 degrees. Therefore, we can set up the following equation to find the value of x:

x + 3x + 90 + 90 = 360

Simplifying the equation, we have:

4x + 180 = 360

Subtracting 180 from both sides, we get:

4x = 180

Dividing both sides by 4, we find:

x = 45

Now that we have the value of x, we can find the obtuse angle by multiplying it by 3:

3x = 3 * 45 = 135

Therefore, the acute angle of the trapezoid is 45 degrees and the obtuse angle is 135 degrees.

Please note that the search results provided did not contain specific information about the angles of a trapezoid with a larger obtuse angle. However, the solution provided above is derived from the properties of a trapezoid and the given information.