Question

ДАЮ ВЫСОКИЙ БАЛЛ! НАДО С РИСУНКОМ! В чотирикутнику АВСД відомо, що АВ=СД, ВС=АД. Кут ВАД=70 градусів. Знайдіть всі кути чотирикутника АВСД,

Answer 1

Ответ:

70°  110°   70°   110°

Объяснение:

Маємо паралелограм АВСД, за умовою протилежні сторони рівні.

Протилежні кути паралелограма рівні, отже ∠С=∠А=70°.

Сума кутів, прилеглих до сторони паралелограма, становить 180°, значить ∠В=∠Д=180-70=110°

Answer 2

Finding the Angles of Quadrilateral ABCD

To find all the angles of quadrilateral ABCD, we can use the given information that AB = CD, BC = AD, and angle BAD = 70 degrees.

Solution:

Given: - AB = CD - BC = AD - Angle BAD = 70 degrees

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

1. Find Angle BCD: - Since BC = AD, and opposite sides of a parallelogram are equal, we can conclude that angle BCD is also 70 degrees. - Therefore, angle BCD = 70 degrees.

2. Find Angle ABC: - Since AB = CD, and opposite sides of a parallelogram are equal, we can conclude that angle ABC is also 70 degrees. - Therefore, angle ABC = 70 degrees.

3. Find Angle ADC: - Since the sum of the angles in a quadrilateral is 360 degrees, we can find angle ADC using the formula: 360 - (angle BAD + angle ABC + angle BCD). - Substituting the given values, we get: 360 - (70 + 70 + 70) = 360 - 210 = 150 degrees. - Therefore, angle ADC = 150 degrees.

4. Find Angle DAB: - Since the sum of the angles in a quadrilateral is 360 degrees, we can find angle DAB using the formula: 360 - (angle ADC + angle BCD + angle ABC). - Substituting the given values, we get: 360 - (150 + 70 + 70) = 360 - 290 = 70 degrees. - Therefore, angle DAB = 70 degrees.

Conclusion:

The angles of quadrilateral ABCD are as follows: - Angle BAD = 70 degrees - Angle BCD = 70 degrees - Angle ABC = 70 degrees - Angle ADC = 150 degrees - Angle DAB = 70 degrees