Question

В равнобедренной трапеции один из углов на 42° меньше другого . Найдите больший угол трапеции .

Answer 1

Finding the larger angle of an isosceles trapezoid

To find the larger angle of an isosceles trapezoid, we need to know the relationship between the two angles. According to the given information, one of the angles is 42° smaller than the other.

Let's assume that the larger angle is represented by x. Since the smaller angle is 42° less than the larger angle, we can represent it as x - 42.

The sum of the interior angles of a trapezoid is 360°. In an isosceles trapezoid, the base angles (the angles formed by the bases and the legs) are congruent. Therefore, we can set up the following equation:

x + (x - 42) + x + (x - 42) = 360

Simplifying the equation, we get:

4x - 84 = 360

Adding 84 to both sides, we have:

4x = 444

Dividing both sides by 4, we find:

x = 111

Therefore, the larger angle of the trapezoid is 111°.