Question

Find the value of X for the given pentagon?

Answer 1

Answer:

x = 44°

Step-by-step explanation:

The sum of the exterior angles of any polygon my be 360°, so just add all the angles up, and subtract this from 360°.

Given a pentagon with exterior angles: 102°, 47°, 34°, and 133° with the missing angle x°.

To find the missing angle, first write an equation representing the given rule:

102° + 47° + 34° + 133° + x° = 360°

(316°) + x° = 360°

316° + x° - 316° = 360° - 316°

x° = 44°.

This way, because the rule must be true, the missing angle with this value will satisfy this:

102° + 47° + 34° + 133° + 44° = 360°

For this topic, here are some general angle rules for polygons:

• n is the number of sides
• 180° (n – 2) = sum of interior angles of any polygon.
• 180° (n – 2) / n = each interior angle of a regular polygon [all sides and or angles the same measure / congruent].
• 360° = sum of exterior angles of any polygon.
• 360° / n = each exterior angle of a regular polygon. [all sides and or angles the same measure / congruent].