Plz solve 15

Plz solve 15 14. A heptagon has three equal angles each of 1200 and four equal angles. Find the size of equal angles. 15. ratio between an exterior angle and the interior angle of a regular polygon is (1) the measure of each exterior angle (it) the measure of each interior angle (iii) the number of sides in the polygon, IVEach interior angle of a regular polygon is double of its exterior angle. Find the number of sides in the polygon. QUADRILATERAL Afour sided polygon is called a quadrilateral. In the adjoining figure, ABCD is a quadrilateral. four sides - AB, BC, CD and DA Four vertices — A, B, C and D Four angles — LA, LB, LC and LD Two diagonals — AC and BD. In quadrilateral ABCD, sides AB, BC; BC, CD; CD, DA; DA, AB are pairs of adjacent sides Sides AB, CD; BC, AD are pairs of opposite sides. Angles ZA, LB; LB, ZC; ZC, ED; ED, LA are pairs of adjacent angles. Angles LA, ZC; LB, ZD are pairs of opposite angles.

Dear Student,

L e t t h e m e a s u r e o f t h e e x t e r i o r a n g l e o f t h e p o l y g o n b e x a n d t h e m e a s u r e o f t h e i n t e r i o r a n g l e o f t h e p o l y g o n b e 5 x . N o w, x + 5 x = 180 ° \Rightarrow 6 x = 180 ° \Rightarrow x = \frac{180 °}{6} \Rightarrow x = 30 ° (i) M e a s u r e o f e a c h e x t e r i o r a n g l e = x = 30 ° (i i) M e a s u r e o f e a c h i n t e r i o r a n g l e o f t h e p o l y g o n = 5 x = 5 \times 30 = 150 ° (i i i) F o r a r e g u l a r p o l y g o n w i t h n s i d e s, m e a s u r e o f e a c h e x t e r i o r a n g l e = \frac{360 °}{n} \Rightarrow 30 ° = \frac{360 °}{n} \Rightarrow n = \frac{360 °}{30 °} \Rightarrow n = 12 T h e p o l y g o n h a s 12 s i d e s

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