Question

Отрезки ab и cd перпендикулярны и пересекаются в точке k. kl биссектриса угла akd. найдите lkb ответ в градусах

Answer 1

-/-/-/--------/-/-/-

Answer 2

Given Information

We are given that line segments AB and CD are perpendicular and intersect at point K. KL is the angle bisector of angle AKD. We need to find the measure of angle LKB in degrees.

Solution

To find the measure of angle LKB, we need to determine the relationship between angle LKB and angle AKD.

Since KL is the angle bisector of angle AKD, it divides the angle into two equal parts. Therefore, angle LKA is equal to angle LKD.

Since line segments AB and CD are perpendicular, angle AKD is a right angle (90 degrees).

Therefore, angle LKA + angle LKB + angle AKD = 180 degrees (the sum of angles in a triangle).

Substituting the given information, we have: angle LKA + angle LKB + 90 degrees = 180 degrees

Since angle LKA is equal to angle LKD, we can rewrite the equation as: 2 * angle LKA + 90 degrees = 180 degrees

Simplifying the equation, we have: 2 * angle LKA = 90 degrees

Dividing both sides of the equation by 2, we get: angle LKA = 45 degrees

Since angle LKA is equal to angle LKD, we can conclude that angle LKB is also equal to 45 degrees.

Therefore, the measure of angle LKB is 45 degrees.