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In the diagram, ABCDE is a regular pentagon.
(a) Calculate /BAE.

(b) What is the name of the quadrilateral ABCD?

(c)The sides AE and CD are produced to meet at X.

(i) Calculate /EDX.

(ii) What type of quadrilateral is BDXE? Explain your answer.

In The Diagram ABCDE Is A Regular Pentagon A Calculate BAE B What Is The Name Of The Quadrilateral ABCD CThe Sides AE And CD Are Produced To Meet At X I Calcula class=

Sagot :

MrRoyalidn

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:

https://brainly.com/question/5715879

#SPJ1

View image MrRoyal
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