Question

Один из углов равнобедренной трапеции равен 105градусов. Найти остальные углы трапеции.

Answer 1

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Answer 2

Finding the Angles of an Isosceles Trapezoid

To find the remaining angles of an isosceles trapezoid when one angle is given as 105 degrees, we can use the properties of trapezoids and the relationships between their angles.

Solution:

Given: - One angle of the isosceles trapezoid = 105 degrees

We can use the fact that the sum of the interior angles of any quadrilateral is 360 degrees, and the opposite angles in an isosceles trapezoid are equal.

Using these properties, we can calculate the remaining angles of the trapezoid.

1. Calculation: - Let's denote the given angle as angle A. - The opposite angle to angle A will also be 105 degrees. - Let's denote the other two angles as B and C.

- Using the fact that the sum of the interior angles of a quadrilateral is 360 degrees, we can calculate the remaining angles: - Angle B = 180 - 105 = 75 degrees. - Angle C = 75 degrees (opposite angles in an isosceles trapezoid are equal).

Result:

The angles of the isosceles trapezoid are: - Angle A = 105 degrees - Angle B = 75 degrees - Angle C = 75 degrees