Using properties of rectangles:
The rectangle has two whole diagonals that intersect to form triangles. As a property of rectangles, diagonals are always congruent. Since the diagonals bisect each other and are congruent, each half of the two diagonals are also congruent. This forms an Isosceles Triangle.
Applying Theorems of Triangles:
If a triangle has a pair of congruent opposite sides leading to the vertex, then the base angles opposite those sides are also congruent. This is the Isosceles Triangle Theorem. So, sides DE and EC are congruent, meaning the two base angles must both measure 31°. Now, we can apply the Triangle Sum Theorem, which states the three interior angles in a triangle sum up to 180°. Let’s create an equation using this theorem to solve for m∠DEC.
Formulating an Algebraic equation:
31+31+m∠DEC=180
Combine like terms:
62+m∠DEC=180
Solve for m∠DEC:
Subtract 62 from both sides:
m∠DEC=180-62
m∠DEC=118
So, the m∠DEC is 118°