Question

PLEASE HELP

Answer 1

Answer:

x = 30° ⇒ (C)

Step-by-step explanation:

If a ray intersects a line at the ray starting point, then

• A pair of linear adjacent angles are formed  

• The sum of the measures of this pair of angles is 180°

∵ The FA intersects the line BE at point A

→ That means a pair of linear adjacent angles are formed, ∠BAF and ∠FAE

∴ m∠BAF and ∠FAE are linear adjacent angles

∴ m∠AFB + m∠FAE = 180°

∵ m∠BAF = 2x° ⇒ given

∵ m∠FAE = 4x° ⇒ given

→ Substitute these values in the equation above  

∴ 2x + 4x = 180

→ Add the like terms in the left side

∴ 6x = 180

→ Divide both sides by 6 to find the value of x

∴ $\frac{6x}{6}=\frac{180}{6}$

∴ x = 30°