For each circle, tangent segments are shown. Use the measurements given find the value of x.
Problem 1 :
Solution:
x = 1/2 (AE - AF)
= 1/2 (141° - 61°)
= 1/2 (80°)
x = 40°
Problem 2 :
Solution:
As per given by property of circle,
∠x = (180 - 70)/2
∠x = 110/2
∠x = 55°
Problem 3 :
Solution:
∠GHI + ∠GBI = 180°
58° + x = 180°
x = 180° - 58°
x = 122°
Problem 4 :
Solution:
Vertical angles are equal.
So, x = 38°
Problem 5 :
Solution:
AB = 160°
So, ∠ADB = 80°
∠ADB = ∠ACD + ∠DAC
So, ∠DAC = 45°
80° = 35° + ∠DAC
∠DAC = 80° - 35°
∠DAC = 45°
∠ABD = ∠DAC
So, x = 45°
Problem 6 :
Solution:
∠AEB = 1/2 ∠AB
= 1/2 × 50
= 25°
∠ABE = 1/2 ∠AE
= 1/2 × (4x + 5)
= (2x + 5/2)°
OA ⊥ DA (DA is a tangent line of circle O)
Hence ∠OAB = 1/2 (180° - 50°)
= 1/2 (130)°
= 65°
∠BAD = 90° - 65° = 25°
Hence, x + 25° = (5/2 + 2x)°
2x - x = 25 - (5/2)
x = 45/2
x = 22.5°
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM