Question

What is the value of x in the diagram below?

A. 88
B. 100
C. 95
D. 151

Answer 1

the figure is four sided so it a heptagon

for a heptagon, the sum of all interior angles is 900°

i.e. x+(x+50°)+(x+50°)+(x+50°)+×+×+(x+50°)=900°

or, 7x+200°=900°

or, 7x=700°

or, x= 100°

Answer 2

The value of x = 100 ⇒ answer B

Explanation:

* Lets study how to find the sum of the interior angles of any polygon

- We can find the sum of the measures of the interior angles of any

polygon using the rule (n - 2) × 180°, where n is the number of its

sides or its angles

* Now lets solve the problem

- The polygon has 7 sides and 7 angles

- The measure of three angles of them is x°

- The measure of four angles of them is (x + 50)°

∵ The sum of the interior angles = (n - 2) × 180°

∵ n = 7

∴ The sum of the interior angles = (7 - 2) × 180° = 5 × 180° = 900°

∵ Three angles each measured x°

∵ Four angles each measured (x + 50)°

∴ 3(x°) + 4(x + 50)° = 900° ⇒ simplify it

∴ 3x + 4(x) + 4(50) = 900 ⇒ add the like terms

∴ 3x + 4x + 200 = 900 ⇒ add the like terms

∴ 7x + 200 = 900 ⇒ subtract 200 from both sides

∴ 7x = 700 ⇒ divide both side by 7

∴ x = 100

* The value of x = 100