Answer:
The value of x is 25
Step-by-step explanation:
- A secant is a line that intersects a circle in exactly two points.
- When two secants, intersect at a point outside a circle then the measure of the angle formed between them is one-half the positive difference of the measures of the intercepted arcs
In the given figure
→ In circle O
∵ GB and GD intersect it at points F, B, and E, D
∴ GB and GD are secants of circle O
∵ GB and GD intersect outside the circle O at point G
∵ They intercepted arcs EF and BD
→ By using the rule above
∴ m∠G = [tex]\frac{1}{2}[/tex] (m arc BD - m arc EF)
∵ m arc BD = m arc BC + m arc CD
∵ m arc BC = 35° and m arc CD = 100°
∴ m arc BD = 35 + 100 = 135°
∵ m arc EF = x
∵ m∠G = 55°
→ Substitute them in the rule above
∴ 55 = [tex]\frac{1}{2}[/tex] (135 - x)
→ Multiply both sides by 2 to cancel the fraction [tex]\frac{1}{2}[/tex]
∵ 110 = 135 - x
→ Subtract 135 from both sides
∴ -25 = -x
→ Divide both sides by -1
∴ 25 = x
∴ The value of x is 25
