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A pentagon has four of its angles equal, If the size of the fifth angle is 60…

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A pentagon has four of its angles equal, If the size of the fifth angle is 60, find the size of each of the four equal angles

A. 108⁰

B. 120⁰

C. 150⁰

D. 60⁰

QUICK ANSWER…

B

DETAILS…

Let each of the four equal angles of the pentagon be represented by x, hence, all the angles will be:

x, x, x, x, and 60

now recall that the sum of all the internal angles of a polygon = 180(n – 2), where n is the number of angles which is 5 in this case. This implies:

x + x + x + x + 60 = 180(5 – 2)

4x + 60 = 180(3)

4x + 60 = 540

4x = 540 – 60

4x = 480

x = 480/4 = 120

Now for the right answer to the above question:

  1. Option A is incorrect.
  2. Option B is correct.
  3. C is not correct.
  4. D is not the correct answer.
RELATED!  The angles marked in the figure above are measured in degrees. Find x?

KEY-POINTS…

You may please note these/this:

  • Sum of all the interior angles of a polygon = 180(n – 2)
  • Sum of all the exterior angles of a polygon = 360
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/ culled from 2020 JAMB-UTME mathematics past question 19 /

A pentagon has four of its angles equal, If the size of the fifth angle is 60... » QuizTablet
A pentagon has four of its angles equal, If the size of the fifth angle is 60... » QuizTablet

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