Question

in the following, figure, ABCDE is a regular pentagon.the sides AB and DC are produced to meet at F. find the angles x y z
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Answer 1

Answer:

x = 36°, y = 36°, z = 72°

Step-by-step explanation:

As we know,

'All inner angles of a regular pentagon value 108°'

∵ ∠B = 108°

Pentagon consists of 3 parts and therefore, each angle values;

108/3 = 36°

∵ y = 36°             (since ∠B = 3y)

ΔEBD is an isosceles Δ and as we know, sum of all the angles of a triangle = 180°

∵ y + z + ∠DEB = 180°

Since isosceles triangles has two equal sides,

z = ∠DEB

⇒ y + z + z = 180°

⇒ y + 2z = 180°

By putting the value of y in the above equation,

36° + 2z = 180°

2z = 180° - 36°

z = 144°/2

z = 72°

Now, x and y are alternate angles

∵ x = y = 36°                       (alternate angles are equal)

Thus, x = 36°, y = 36° , and z = 72°