Question

Кути рівнобічної трапеції відносяться як 5:4.Знайти всі кути трапеції

Answer 1

Сумма углов при одной боковой стороне у трапеции равна 180°
5х + 4х = 180
9х = 180
х = 20
и сами углы 5х = 100°, 4х = 80°

Answer 2

Finding the Angles of an Isosceles Trapezoid

To find all the angles of an isosceles trapezoid, we need to know the ratio of the lengths of the non-parallel sides. In this case, the ratio is given as 5:4. However, the search results provided do not directly address the question or provide specific information about the angles of an isosceles trapezoid with a 5:4 ratio.

To find the angles of an isosceles trapezoid, we can use the fact that the opposite angles are congruent. Let's denote the angles as A, B, C, and D, with A and B being the acute angles and C and D being the obtuse angles.

Since the trapezoid is isosceles, we know that angle A is congruent to angle B and angle C is congruent to angle D. Let's denote the measure of angle A as x.

Using this information, we can set up the following equations:

Angle A + Angle B + Angle C + Angle D = 360 degrees (sum of angles in a quadrilateral) x + x + Angle C + Angle D = 360 degrees

Since angle C is congruent to angle D, we can rewrite the equation as:

2x + 2(Angle C) = 360 degrees

Simplifying the equation, we have:

2x + 2x = 360 degrees 4x = 360 degrees x = 90 degrees

Therefore, angle A and angle B are both 90 degrees, and angle C and angle D are also 90 degrees.

In conclusion, all the angles of an isosceles trapezoid with a 5:4 ratio are 90 degrees.

Please note that the search results provided did not directly address the question, so the answer is based on the properties of an isosceles trapezoid.