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Question
The angles of a pentagon are 100°, 96°, 74°, 2x° and 3x°. Find the measures of the two angles 2x° and 3x°.
Solution
A pentagon has 5 sides
∴ Sum of interior anfles
= (n - 2) x 180°
= (5 - 2) x 180°
= 3 x 180°
= 540°
Given, the angles are 100°, 96° 74°, 2x° and 3x°
∴ 100° + 96° 74° + 2x° + 3x° = 540°
⇒ 5x° + 270° = 540°
⇒ x = `((540° - 270°))/(5)` = 54°
∴ The two angles 2x° and 3x° are 108° and 162° respectively.
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