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.

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Updated on: 10-Oct-2022

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