Question

CDEF is a rectangle. Find the angles a and b, if ∠DCE = 32°.

Answer 1

Given:

• CDEF is a rectangle.
• ∠DCE = 32°.
• Need to find angles a and b.

Step-wise calculation:

1. In rectangle CDEF, diagonals CE and DF intersect, creating triangles within the rectangle.

2. Since it’s a rectangle, angles at vertices like C and F are right angles (90°).

3. Triangle DCE involves angle ∠DCE = 32°.

4. Angle a at point E in triangle CDE is found by angle sum property:

Triangle CDE is right angled at D (90°).

Sum of angles in triangle CDE = 180°, so a = 180° – 90° – 32° = 58°.

5. To find angle b at F:

By symmetry, angle b is complementary to angle at C.

Angle b = 32° equal to ∠DCE because diagonals in a rectangle create congruent angles at opposite vertices.

Angle a = 58°

Angle b = 32°