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Question
The angles of a pentagon are in the ratio 2 : 5 : 6 : 4 : 3. The largest angle is ______.
Options
54°
135°
162°
108°
MCQ
Fill in the Blanks
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Solution
The angles of a pentagon are in the ratio 2 : 5 : 6 : 4 : 3. The largest angle is 162°.
Explanation:
The sum of the interior angles of a pentagon is given by (5 − 2) × 180° = 540°. Given that the angles are in the ratio 2 : 5 : 6 : 4 : 3, let the angles be 2x, 5x, 6x, 4x, and 3x. Setting up the sum gives:
2x + 5x + 6x + 4x + 3x = 540°
20x = 540°
x = 27°
The largest angle corresponds to the ratio part 6:
Largest angle = 6 × 27° = 162°
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