Answer:
The value of x is 17
Step-by-step explanation:
From the given figure
∵ AD ∩ BE at point C
∴ ∠ACB and ∠DCE are vertically opposite angles
∵ The vertically opposite angles are equal in measures
∴ m∠ACB = m∠DCE
→ The sum of interior angles of any Δ is 180°
∴ m∠A + m∠B + m∠ACB = 180°
∴ m∠D + m∠E + m∠DCE = 180°
→ Since the right sides equal, then equate the left sides
∵ m∠A + m∠B + m∠ACB = m∠D + m∠E + m∠DCE
→ Cancel the two equal angles ACB and DCE
∴ m∠A + m∠B = m∠D + m∠E
∵ m∠A = 4x, m∠B = 49°
∵ m∠D = 100°, m∠E = x
→ Substitute them in the equation above
∴ 4x + 49 = 100 + x
→ Subtract x from both sides
∵ 4x - x + 49 = 100 + x - x
∴ 3x + 49 = 100
→ Subtract 49 from both sides
∴ 3x + 49 - 49 = 100 - 49
∴ 3x = 51
→ Divide both them by 3 to find x
∵ [tex]\frac{3x}{3}[/tex] = [tex]\frac{51}{3}[/tex]
∴ x = 17
∴ The value of x is 17
