Question

50 POINTS GIVING BRAINLIEST

Answer 1

Answer:

x = 37°

x = 40°

x = 260°

Step-by-step explanation:

To find angle x when two secants or tangents intersect outside the circle, simply subtract the smaller arc from the bigger arc and half the result.

Question 1

$x=\dfrac12(128^{\circ}-54^{\circ})=37^{\circ}$

Question 2

To find the bigger arc, subtract the smaller arc from 360°

⇒ 360° - 140° = 220°

$x=\dfrac12(220^{\circ}-140^{\circ})=40^{\circ}$

Question 3

The smaller arc can also be found by subtracting the external angle from 180°

Smaller arc = 180° - 80° = 100°

$80^{\circ}=\dfrac12(x-100^{\circ})$

$160^{\circ}=x-100^{\circ}$

$x=260^{\circ}$

Answer 2

#1

• 2x=128-54
• 2x=74
• x=37°

#2

Bigger Arc=360-140=220°

• 2x=(220-140)
• 2x=80
• x=40°

#3

Smaller arc=180-80=100°

• 2(80)=x-100
• 160=x-100
• x=260°