Question

?In a pentagon the measure of four angles are equal. If the measure of the 5th angle is 120° then what is each equal angle *​

Answer 1

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In a pentagon the measure of four angles are equal. If the measure of the 5th angle is 120° then what is each equal angle?

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Given,

One angle of a pentagon = 120°

Let remaining four angles be x, x, x and x

∴ Their sum will be:

➩ 4x + 120° = 540°

(We know, sum of the interior angles of a pentagon is 540 degrees.)

➩ 4x = 540° – 120°

➩ 4x = 420°

➩ x = 105°

Therefore,

✮ Measure of each equal angles are 105° .

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Answer 2

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One angle of a pentagon = 120° Let remaining four angles be x, x, x and x Their sum = 4x + 120° But sum of all the interior angles of a pentagon

= (2n – 4) x 90°

= (2 x 5 – 4) x 90°= 540°

= 3 x 180° = 540°

∴ 4x + 120° = 540°

4x = 540° – 120°

4x = 420

x = (420/4)°

⇒ x = 105°

∴Equal angles are 105° (Each)