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The diagram shows a rhombus inside a regular pentagon.
Work out the size of angle x.

The diagram shows a rhombus inside a regular pentagon. Work out the size of angle-example-1
User Khaly
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1 Answer

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14 votes

Based on the diagram showing a rhombus inside a regular pentagon, the size of angle x is 18°.

In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

Sum of interior angles = 180 × (5 - 2)

Sum of interior angles = 180 × 3

Sum of interior angles = 540°.

Therefore, the measure of each interior angle is given by;

Interior angle of a pentagon = 540°/5

Interior angle of a pentagon = 108°

A rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent, with a measure of 90 degrees;

x + 90 = 108

x = 108 - 90

x = 18°

User LittleBit
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