# PAIR OF ANGLES WORKSHEET

Problem 1 :

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

Problem 2 :

In the figure shown below, let the lines l1 and lbe 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.

Problem 1 :

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

 Vertically opposite angles are congruent. < 1  =  < 3< 2  =  < 4< 5  =  < 7< 6  =  < 8
 Corresponding angles are congruent. < 1  =  < 5< 2  =  < 6< 3  =  < 7< 4  =  < 8
 Alternate interior  angles  are equal. < 3  =  < 5< 4  =  < 6
 Alternate exterior angles  are equal. < 1  =  < 7< 2  =  < 8

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

3x  =  390

Divide each side by 3.

x  =  130

So, the value of x is 130.

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