In the trapezoid, the larger base is 18 cm, the angles for the larger base are 53 and 37.

In the trapezoid, the larger base is 18 cm, the angles for the larger base are 53 and 37. Find the distance from the point of intersection of the extensions of the lateral sides to the middle of the larger base.

Consider the resulting triangle, consisting of the base of the trapezoid, and the extended two lateral sides. Let’s calculate the angle between these sides, knowing the angles at the base of the trapezoid.
The angle at the apex of the triangle is (180 ° – 53 ° – 37 °) = 90 °.
The resulting triangle is rectangular, the hypotenuse is 18 cm.
And the segment connecting the vertex of the right angle with the middle of the hypotenuse is the median, which is equal to half of the hypotenuse. This is the property of the median in a right-angled triangle drawn to the hypotenuse.

That is, the required segment is 18/2 = 9 (cm).