the diagram shows a convex polygon.\nwhat is the value of x?\nx = \\square^\\circ

Explanation:

Step1: Recall exterior angle sum of polygon

The sum of exterior angles of any convex polygon is (360^\circ). So we sum all given exterior angles and set equal to (360^\circ). ((2x - 50) + (2x - 49) + (3x - 3) + 2x + 57 = 360)

Step2: Combine like terms

Combine the (x)-terms and constant terms: ((2x + 2x + 3x + 2x) + (-50 - 49 - 3 + 57) = 360) (9x + (-45) = 360)

Step3: Solve for (x)

Add 45 to both sides: (9x = 360 + 45) (9x = 405) Divide both sides by 9: (x = \frac{405}{9}) (x = 45)

Answer:

(45)