Question

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1. Find x in the following figures. (Picture in attachment )

2. Find the number of sides of a regular polygon whose each exterior angle has a measure of 45°.


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Answer 1

Answer:

1. No attachment??

2.

Sum of the exterior angles of regular polygon =360°

But each exterior angle = 45°

Number of sides of regular polygon =

360°/45°

=8

Hope it helps you

Answer 2

Questions :

1. Find x in the following figures.

2. Find the number of sides of a regular polygon whose each exterior angle has a measure of 45°.

Solutions :

1) As we know that two exterior angles are both 125°

Interior angle + Exterior angle = 180°

[They lie on the same line]

Both interior angles = 180° - 125° = 55°

Hence, sum of two interior angles = 55° × 2 = 110°

We know that,

Sum of three angles of a triangle is 180°

Thus the third angle will be = 180° - 70° = 110°

Therefore, x is 180° - 70° = 110°

2) Measure of all ext. angles= 360°

Each angle = 45°

No of sides regular polygon has = 360°/45° = 8

Hence, 8 sides in a regular polygon

Final Answers :

• 1) x is 110°

• 2) 8 sides of a polygon