Calculate angle DEF

Question

Triangle DEF has vertices D(-3,5), E(2,3) and F(6,7). Calculate angle DEF. 

Answer 1

calculate the slope of DE. It's -2/5 = -0.4

slope of EF = 1

angle of EF with the horizontal is 45 degrees

for the angle of ED with the horizontal find the angle whose sine is 0.4

angle of ED with the horizontal is 23,56716747 = about 23.6 degrees rounded off to one decimal place

add them to get 68.6 degrees

180-68.6 = 111.4 degrees = angle DEF

draw a rough sketch, plot the points and connect the points into a triangle. It definitely looks greater than 90 degrees, no matter how sloppy you do it. 111.4 looks about right.