what does the angles of a reactagle equal when split up into for trianglular regions

Question

If angle EDC is 32° and E is the midpoint of all the sides what is the measures of all other angles.

 

Thank you!

Answer 1

If we draw two diagonals in the rectangle, we will have four triangles within the rectangle.  Two of them will be congruent to each other, since a rectangle has two pairs of equal parallel sides. Also, the adjacent sides of a rectangle form 90 degrees.  E is the midpoint of all sides, makes point E the center of the rectangle.  Diagonals AC and BD intersect at point E and are equal to each other in length. 

 

Based on this, our triangles are AEB, BEC, CED, and AED.   One more thing to notice is that these four triangles are isosceles, which means that two of the angles are congruent to each other.  If you know one angle of the triangle, then you know the angle of another.

 

The sum of the angles in a triangle equal 180 degrees.

The sum of the angles of complementary angles is 90 degrees.

 

 

Now that you have the information given to you, draw the figure on your own and use it to find the missing angles.