Question

How do I find b,c and d? A is 108°

Answer 1

• ∠B = 72°
• ∠C = 36°
• ∠D = 144°

Explanation:

First, we must find the total amount of degrees in the pentagon shape.

• => 180(n - 2)
• => 180(5 - 2)
• => 180(3)
• => 540

Hence, the amount of degrees in the pentagon shape is 540°.

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You have stated that A is 108°.

Check:

• => 540 ÷ 5
• => 108°

Hence, it is proven that this pentagon is a regular pentagon. With that, we are given a clue to find ∠B.

• => 180 = 108 + ∠B
• => ∠B = 72

Hence, the value of ∠B is 72°

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Since ∠B is 72°, we know that the angle in the top left of the triangle is also 72. The triangles sum up-to 180°.

• => 72 + 72 + c = 180°
• => 144 + c = 180°
• => ∠C = 36

Hence, the value of ∠C is 36°.

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We have got a clue, let's use that clue to solve ∠D.

• => 180 = 36 + ∠D
• => -36 + 180 = ∠D
• => 144 = ∠D

Hence, the value of ∠D is 144°.

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`BrainiacUser1357`

Answer 2

b = 72

c = 36

d = 144

Explanation:

As every angle in the pentagon are equal (the lines inside every angle mean they are equal), angles on a straight line must add up to 180° ∴

A = 108°

108 + b = 180

180 - 108 = b

72 = b

As the top left angle of the triangle is also on a straight line with one of these angles, the value of this angle is also 72°.

All angles in a triangle must add up to 180° ∴

72 + 72 + c = 180

144 + c = 180

c = 180 - 144

c = 36

Angles on a straight line must add to 180° ∴

d + c = 180

d + 36 = 180

d = 180 - 36

d = 144

Hope this helps!