# ANGLE RELATIONSHIPS IN CIRCLES WORKSHEET

## About "Angle Relationships in Circles Worksheet"

Angle Relationships in Circles Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on angle relationships in circles.

Before look at the worksheet, if you would like to know the stuff related to angle relationships in circles,

## Angle Relationships in Circles Worksheet - Problems

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 mCBD. 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.  ## Angle Relationships in Circles Worksheet - Solutions

Problem 1 :

Line m is tangent to the circle. Find the measure of the red angle. Solution :

m∠1  =  1/2 ⋅ 150°

m∠1  =  75°

Problem 2 :

Line m is tangent to the circle. Find the measure of the red arc. Solution :

m∠arc RSP  =  2 ⋅ 130°

m∠arc RSP  =  260°

Problem 3 :

In the diagram below, BC is tangent to the circle.  Find mCBD. Solution :

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. Solution :

x°  =  1/2 ⋅ (m∠arc PS + m∠arc RQ)

x°  =  1/2 ⋅ (106° + 174°)

x°  =  1/2 ⋅ (280°)

x°  =  140°

Hence, the value of x is 140.

Problem 5 :

Find the value of x in the diagram shown below. Solution :

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. Solution :

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 After having gone through the stuff given above, we hope that the students would have understood, "Angle Relationships in Circles Worksheet".

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