Question

the diagram shows a convex polygon.
111°
150°
129°
4x−38°
3x
3x+28°
3x
what is the value of x?
x =

Explanation:

Step1: Count polygon sides

The polygon has 7 sides (heptagon).

Step2: Calculate total interior angles

Formula: $(n-2)×180°$, $n=7$.
Total = $(7-2)×180°=900°$.

Step3: Sum known angles and expressions

Sum = $129 + 111 + 150 + (4x-38) + (3x+28) + 3x + 3x$.
Simplify: $129+111=240$, $240+150=390$, $390-38=352$, $352+28=380$;
Variables: $4x+3x+3x+3x=13x$.
Total sum: $13x + 380$.

Step4: Solve for x

Set equal to 900: $13x + 380 = 900$.
$13x = 900 - 380 = 520$.
$x = 520÷13 = 40$.

Answer:

40