Question

The convex polygon below has 7 sides. find the value of x

Answer 1

x = 147

Explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 7 , then

sum = 180° × 5 = 900°

sum the interior angles and equate to 900

x + 141 + 112 + 129 + 106 + 139 + 126 = 900

x + 753 = 900 ( subtract 753 from both sides )

x = 147

Answer 2

The given convex polygon has 7 sides

Hence its sum of interior angles is given by the formula , (number of sides-2)x180°

=> (7-2) x 180°

=> 5 x 180°

=> 900°

The sum of all angles must be equal to 900°

The given six angles are :

139°,126°,106°,129°,141°,112° , x°

=> 139+126+106+129+141+112+x = 900°

=> 753 + x = 900

=> x = 900-753

=> x = 147°

Hence 147° is the required answer.