**Understanding Quadrilaterals**

**Question 1.****Find x in the following figures.**

**Solution.**

We know that the sum of the exterior angles formed by producing the sides of a convex polygon in the same order is equal to 360°. Therefore,

**(a)**x + 125° + 125° = 360°

⇒ x + 250° = 360°

⇒ x = 360° – 250° = 110°

**(b)**x + 90° +60° + 90° + 70° = 360°⇒ x + 310° = 360°

⇒ x = 360° – 310° = 50°

**Question 2.****Find the measure of each exterior angle of a regular polygon of(i)** 9 sides

**(ii)**15 sides

**Solution.****(i)** Each exterior angle of a regular polygon of 9 sides

**(ii)** Each exterior angle of a regular polygon of 15 sides

**Question 3.****How many sides does a regular polygon have if the measure of an exterior angle is 24°?**

**Solution.**

Since the number of sides of a regular polygon

**Question 4.****How many sides does a regular polygon have if each of its interior angles is 165°?**

**Solution.**

Let there be n sides of the polygon. Then, its each interior angle

Thus, there are 24 sides of the polygon.

**Question 5.****(a)** Is it possible to have a regular polygon with measure of each exterior angle as 22°?**(b)** Can it be an interior angle of a regular polygon ? Why?

**Solution.****(a)** Since the number of sides of a regular polygon

= ,

Which is not a whole number.

A regular polygon with measure of each exterior angle as 22° is not possible.

**(b)** If interior angle = 22°, then its exterior angle = 180° – 22° = 158°.

But 158 does not divide 360 exactly.

Hence, the polygon is not possible.

**Question 6.****(a)** What is the minimum interior angle possible for a regular polygon? Why?**(b)** What is the maximum exterior angle possible for a regular polygon?

**Solution.****(a)** The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle = 60°.**(b)** Since the minimum interior angle of a regular polygon is equal to 60°, therefore, the maximum exterior angle possible for a regular polygon = 180° – 60° – 120°.