What are the coordinates of the point on the directed line segment from (−9,−10) to (-5, -2) that partitions the segment into a ratio of 5 to 3?

Step-by-step explanation:

Find the diagram attached

From the given diagram, since AB is parallel to CD, this means both lines have similar properties.

For the triangle GEF, AFB, ∠GEF = ∠GED - ∠FED

Given ∠GED = 135 and ∠FED = 90

∠GEF = 135-90

∠GEF = 45°

Also, sum of angle in the triangle GEF is 180°, hence;

∠GEF + ∠EGF + ∠GFE = 180°

45°+∠EGF+90° = 180°

∠EGF+135° = 180°

∠EGF = 180-135

∠EGF = 45°

since the sum of angle on the straight line AGF = 180°, then;

∠AGE+∠EGF = 180°

∠AGE+45° = 180°

∠AGE = 180°-45°

∠AGE = 135°

Hence the value of ∠AGE is 135°