PAIR OF ANGLES WORKSHEET

Problem 1 :

In the figure shown below,  let the lines l₁ and l₂ be parallel and t is transversal. Find the value of x.

Problem 2 :

In the figure shown below, let the lines l₁ and l₂ be parallel and m is transversal. Identify the pairs of angles which are congruent. 

Problem 3 :

Find the value of x :

Problem 4 :

Find the value of x : 

Problem 5 :

Find the conjugate of the angle measure 97°. 

Problem 6 :

If (x + 30)° and (2x - 60)° are conjugate, find the value of x.  

Detailed Answer Key

Problem 1 :

In the figure shown below,  let the lines l₁ and l₂ be parallel and t is transversal. Find the value of x.

Solution : 

From the given figure, 

∠(2x + 20)° and ∠(3x - 10)° are corresponding angles. 

So, they are congruent. 

Then, 

2x + 20  =  3x - 10

30  =  x

Problem 2 :

In the figure shown below, let the lines l₁ and l₂ be parallel and m is transversal. Identify the pairs of angles which are congruent. 

Problem 3 :

Find the value of x :

Solution :

From the picture above, it is clear that the angles (x+1), (x-1) and (x+3) are complementary.  

Then,

(x+1) + (x-1) + (x+3)  =  90

x + 1 + x - 1 + x + 3  =  90

Simplify.

3x + 3  =  90

Subtract 3 from each side. 

3x  =  87

Divide each side by 3.

x  =  29

So, the value of x is 29.

Problem 4 :

Find the value of x :

Solution :

From the picture above, it is clear (5x+4), (x-2) and (3x+7) are supplementary angles. 

Then, 

(5x+4) + (x-2) + (3x+7)  =  180

5x + 4 + x -2 + 3x + 7  =  180

Simplify. 

9x + 9  =  180

Subtract 9 from each side.

9x  =  171

Divide each side by 9.

x  =  19

So, the value of x is 19.

Problem 5 :

Find the conjugate of the angle measure 97°. 

Solution : 

Let x° be the conjugate of the angle measure 97°. 

Because x° and 97° are conjugate, their sum equals 360°.

Then, 

x° + 97°  =  360°

Subtract 97° from each side. 

x°  =  263°

So, the conjugate of the angle measure 97° is 263°. 

Problem 6 :

If (x + 30)° and (2x - 60)° are conjugate, find the value of x.  

Solution : 

Because (x + 30)° and (2x - 60)° are conjugate, their sum equals 360°.

Then, 

(x + 30)° + (2x - 60)°  =  360°

x + 30 + 2x - 60  =  360

Simplify.

3x - 30  =  360

Add 30 to each side. 

3x  =  390

Divide each side by 3.

x  =  130

So, the value of x is 130.

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