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1. Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1: 5
2. PQRSTU is a regular hexagon. Determine each angle of triangle PQT.
To find:
1. We have to determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1: 5
2. We have to determine each angle of triangle PQT if PQRSTU is a regular hexagon.
Solution:
1)
Sum of interior angles of polygon =$ (2n - 4) \times 90$
Sum of interior angles = $5 \times$ sum of exterior angles = $5 \times 360$
$(2n - 4) \times 90 = 5 \times 360$
$2n - 4 = 5 \times \frac{360}{90} = 20$
or $2n = 24$ or $n = 12$
So the required polygon has 12 sides.
2)
Exterior angle of regular hexagon = $\frac{360}{6} = 60$;
Interior angle of regular hexagon =$180 - 60 = 120$
From triangle PQT
The angles are 30, 30, and 120.