Question

Найдите углы прямоугольной трапеции диагональ которой делит тупой угол трапеции пополам и образует с ее меньшей боковой стороной угол 20°

Answer 1

1 угол = 90°
2 угол=90° 
3 угол=115°
4 угол=65°

Answer 2

Finding the angles of a right trapezoid

To find the angles of a right trapezoid, we need to consider the properties of the trapezoid and the given information. Let's break down the problem step by step.

1. We are given that the diagonal of the trapezoid divides the obtuse angle of the trapezoid in half. 2. We are also given that the diagonal forms a 20° angle with the smaller lateral side of the trapezoid.

Let's denote the trapezoid as ABCD, where AB is the longer base, CD is the shorter base, and AD and BC are the lateral sides.

To find the angles of the trapezoid, we can use the following steps:

1. Identify the obtuse angle of the trapezoid. Since the diagonal divides this angle in half, we can denote it as ∠BAC. 2. Use the given information that the diagonal forms a 20° angle with the smaller lateral side of the trapezoid. Denote this angle as ∠CDB.

Now, let's find the angles of the trapezoid:

1. The sum of the angles in a trapezoid is 360°. Since we know that the trapezoid is right, we can determine that one of the angles is 90°. 2. Since the diagonal divides the obtuse angle (∠BAC) in half, we can determine that ∠BAC = 2 * ∠CDB. 3. We are given that ∠CDB = 20°. Therefore, ∠BAC = 2 * 20° = 40°. 4. Since the sum of the angles in a triangle is 180°, we can find the remaining angle ∠BCA = 180° - 90° - 40° = 50°.

Therefore, the angles of the right trapezoid are: - ∠BAC = 40° - ∠BCA = 50° - ∠CDB = 20° - ∠CDA = 90° - ∠ADB = 90°

Please note that the above solution is based on the given information and the properties of a right trapezoid.