# If One Angle of a Pentagon is 120° and Each of the Remaining Four Angles is X°, Find the Magnitude of X. - Mathematics

Sum

If one angle of a pentagon is 120° and each of the remaining four angles is x°, find the magnitude of x.

#### Solution

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+120o° = 540°

4x = 540° – 120°

4x = 420

x = 420/4 => "x" = 105°

∴ Equal angles are 105° (Each)

Concept: Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
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#### APPEARS IN

Selina Class 6 Mathematics
Chapter 28 Polygons
Exercise 28 (A) | Q 8
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