Answer:
The value of x is 25
Step-by-step explanation:
- <em>A secant is a line that intersects a circle in exactly two points. </em>
- <em>When </em><em>two secants, intersect at a point outside a circle</em><em> then the </em><em>measure of the angle formed between them is one-half the positive difference of the measures of the intercepted arcs</em>
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 = (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 = (135 - x)
→ Multiply both sides by 2 to cancel the fraction
∵ 110 = 135 - x
→ Subtract 135 from both sides
∴ -25 = -x
→ Divide both sides by -1
∴ 25 = x
∴ The value of x is 25