The shape ABCDE is a regular pentagon with five sides, such that the five sides are congruent
Part A: Calculate ∠BAE
The angle BAE is a vertex angle, and it is calculated using:
BAE = 180 * (n - 2)/n
Where n= 5; i.e. the number of sides.
This gives:
BAE = 180 * (5 - 2)/5
Evaluate
BAE = 108°
Hence, the measure of angle BAE is 108°
Part B: The name of the quadrilateral ABCD
When the vertices A and B are joined together, the shape becomes a trapezoid.
Hence, the name of the quadrilateral ABCD is a trapezoid.
Part C (i) Calculate ∠EDX
See attachment for the new figure.
From the attached figure, we have:
∠EDX + ∠EDC = 180° ---- the sum of angles on a straight line
Where:
∠EDC = ∠BAE = 108°
So, we have:
∠EDX + 108° = 180°
Subtract 108° from both sides
∠EDX = 72°
Hence, the measure of angle EDX is 72 degrees
Part C (ii) What type of quadrilateral is BDXE?
The quadrilateral BDXE is a parallelogram.
This is so because the opposite sides of BDXE are parallel, but not congruent
Read more about quadrilaterals at:
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