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

Step-by-step explanation:

Question :

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°.

Solution :

1.

Sum of all the exterior angles of a polygon = 360°

➠ 125° + 125° + x° = 360°

➠ 250° + x° = 360°

➠ x° = 360° - 250°

➠ x° = 110°

∴ Value of x is 110°.

2.

Total measure of all exterior angles = 360°

Measure of each exterior angle = 45°

The number of exterior angles =

$\displaystyle{ \implies \frac{ \cancel{360}}{ \cancel{45}} }$

$\displaystyle{ \implies \: 8}$

∴ The polygon has 8 sides.

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