Question

Отрезки AD и BC пересекаются в точке О и расположеы так, что прямые АВ и CD параллельны. Известно, что угол ОАВ=32 градусам, угол ОВА=28 градусам. Найдите угол OCD.(через признаки параллельности,а не через сумму углов в треугольнике)

Answer 1

Угол OCD равный углу OBA и равный 28 градусов, как угол при двох параллельных прямых и сечной CB

Answer 2

OCD равен углу OBA и равен 28 градусов, так как эти углы внутренние накрест лежащие при параллельных прямых AB иCD и секущей BC

Answer 3

Solution: Finding the Angle OCD

To find the angle OCD, we can use the properties of parallel lines and transversals. When a transversal intersects two parallel lines, several pairs of corresponding angles are formed. One of these pairs is the pair of alternate interior angles.

Given: - Angle OAB = 32 degrees - Angle OBA = 28 degrees

We can use the properties of alternate interior angles to find the measure of angle OCD.

Using Alternate Interior Angles

When a transversal intersects two parallel lines, the alternate interior angles are congruent. In this case, the transversal is line OB, and the parallel lines are AB and CD.

Therefore, we can conclude that: - Angle OAB is alternate to angle OCD - Angle OBA is alternate to angle ODC

So, angle OCD is congruent to angle OAB, and angle ODC is congruent to angle OBA.

Calculating the Angle OCD

Given that angle OAB = 32 degrees, we can conclude that angle OCD is also 32 degrees, as they are alternate interior angles.

Therefore, angle OCD = 32 degrees.

This approach uses the properties of parallel lines and transversals to find the measure of angle OCD without relying on the sum of angles in a triangle.