State exterior angle theorem

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.

The ratio between the interior angle and the exterior angle of a regular polygon is 2: 1. Find : (i) each exterior angle of the polygon. (ii) number of sides in the polygon.

Calculate the number of sides of a regular polygon, if (i) its interior angle is five times its exterior angle. (ii) the ratio between its exterior angle and interior angle is 2:7. (iii) its exterior angle exceeds its interior angle by 60^@ .

(Exterior Angle Theorem): If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles. GIVEN : A triangle A B C,D is a point of B C produced, forming exterior angle /_4. TO PROVE : /_4=/_1+/_2 i.e. , /_A C D=/_C A B+/_C B Adot

If the difference between an exterior angle of a regular polygon of 'n' sides and an exterior angle of another regular polygon of '(n+1)' sides is equal to 5^(@) , find the value of 'n'.

The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.

Two alternate sides of a regular polygon, when produced, meet at right angle. Find: the value of each exterior angle of the polygon.

The side B C of a A B C is produced on both sides. Show that the sum of the exterior angles so formed is greater than /_A by two right angles.

The side B C of a A B C is produced on both sides. Show that the sum of the exterior angles so formed is greater than /_A by two right angles.

AB, BC and CD are the three consecutive sides of a regular polygon. If angleBAC= 15^(@) , find, each exterior angle of the polygon