Problem 1 :
Line m is tangent to the circle. Find the measure of the red angle.
Problem 2 :
Line m is tangent to the circle. Find the measure of the red arc.
Problem 3 :
In the diagram below, BC is tangent to the circle. Find m∠CBD.
Problem 4 :
Find the value of x in the diagram shown below.
Problem 5 :
Find the value of x in the diagram shown below.
Problem 6 :
Find the value of x in the diagram shown below.
Problem 1 :
Line m is tangent to the circle. Find the
measure of the red angle.
Answer :
m∠1 = 1/2 ⋅ 150°
m∠1 = 75°
Problem 2 :
Line m is tangent to the circle. Find the measure of the red arc.
Answer :
m∠arc RSP = 2 ⋅ 130°
m∠arc RSP = 260°
Problem 3 :
In the diagram below, BC is tangent to the circle. Find m∠CBD.
Answer :
m∠ CBD = 1/2 ⋅ m∠arc DAB
5x = 1/2 ⋅ (9x + 20)
Multiply each side by 2.
10x = 9x + 20
Subtract 9x from each side.
x = 20
So, the angle measure CBD is
m∠ CBD = 5(20°)
m∠ CBD = 100°
Problem 4 :
Find the value of x in the diagram shown below.
Answer :
x° = 1/2 ⋅ (m∠arc PS + m∠arc RQ)
x° = 1/2 ⋅ (106° + 174°)
x° = 1/2 ⋅ (280°)
x° = 140°
So, the value of x is 140.
Problem 5 :
Find the value of x in the diagram shown below.
Answer :
Using Theorem 2, we have
m∠ GHF = 1/2 ⋅ (m∠EDG - m∠GF)
72° = 1/2 ⋅ (200° - x°)
Multiply each side by 2.
144 = 200 - x
Solve for x.
x = 56
Problem 6 :
Find the value of x in the diagram shown below.
Answer :
Arcs MN and MLN make a whole circle. So, we have
m∠arc MLN + m∠MN = 360°
Plug m∠MN = 92°.
m∠arc MLN + 92° = 360°
Subtract 92° from each side.
m∠arc MLN = 360° - 92°
m∠arc MLN = 268°
Using Theorem 2, we have
x° = 1/2 ⋅ (m∠MLN - m∠MN)
x° = 1/2 ⋅ (268° - 92°)
x = 1/2 ⋅ (176)
x = 88
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