1. **Stating the problem:** We have a quadrilateral C D E G formed by a parallelogram C D F G and a triangle D F E. (a) We need to identify the type of quadrilateral C D E G. (b) We need to find the size of angle D F E in the triangle. 2. **Given information:** - Parallelogram C D F G has angle C = 136°. - Opposite sides of the parallelogram are equal: C G = D F and C D = F G. - Quadrilateral C D E G is formed by adding triangle D F E to the parallelogram. 3. **Step (a): Name of the quadrilateral C D E G** - Since C D F G is a parallelogram and E is a point outside it forming triangle D F E, the quadrilateral C D E G is a kite. - This is because two pairs of adjacent sides are equal: C D = F G and C G = D F, and the shape is formed by joining a parallelogram and a triangle sharing side D F. 4. **Step (b): Work out angle D F E** - In parallelogram C D F G, adjacent angles are supplementary. - Given angle C = 136°, angle D = 180° - 136° = 44°. - Angle D in parallelogram is angle C D F, so angle C D F = 44°. - Triangle D F E shares side D F with parallelogram. - Since C G = D F, and C G is parallel to D F, angle at F in triangle D F E is supplementary to angle at G in parallelogram. - Angle G in parallelogram equals angle C = 136° (opposite angles equal). - Therefore, angle F in triangle D F E = 180° - 136° = 44°. - Triangle D F E has angles: angle D F E = ?, angle F E D = ?, angle E D F = ? - Since D F E is the angle at vertex F, and we found it to be 44°. **Final answers:** - (a) Quadrilateral C D E G is a kite. - (b) Angle D F E = 44°.