CORRESPONDING ANGLES POSTULATE

Corresponding Angles :

Corresponding angles are the angles which are formed when two parallel lines are cut by a transversal. 

In the figure above, the following pairs of angles are corresponding angles. 

∠1 and ∠5

∠2 and ∠6

∠4 and ∠8

∠3 and ∠7

Corresponding Angles Postulate :

When two parallel lines are cut by a transversal, the corresponding angles in the intersection region are congruent. 

In the figure above, 

∠1 ≅ ∠5

∠2 ≅ ∠6

∠4 ≅ ∠8

∠3 ≅ ∠7

Corresponding Angles Postulate - Converse

When two lines are cut by a transversal, if the corresponding angles in the intersection region have equal measure, then the two lines are parallel.  

In the figure above, lines m and n are parallel. Because, a pair of corresponding angles have equal measure. 

Solved Problems

Problem 1 :

In the figure shown below, m∠1 = 105°. Find the measures of the remaining angles.

Solution : 

∠1 and ∠2 form a linear pair and they are supplementary. 

m∠1 + m∠2  =  180°

105° + m∠2  =  180°

m∠2  =  75°

∠1 and ∠3 are vertical angles and they are equal. 

m∠3  =  m∠1

m∠3  =  105°

∠2 and ∠4 are vertical angles and they are equal. 

m∠4  =  m∠2

m∠4  =  75°

∠1 and ∠5 are corresponding angles and they are equal.

m∠5  =  m∠1

m∠5  =  105°

∠2 and ∠6 are corresponding angles and they are equal.

m∠6  =  m∠2

m∠6  =  75°

∠3 and ∠7 are corresponding angles and they are equal.

m∠7  =  m∠3

m∠7  =  105°

∠4 and ∠8 are corresponding angles and they are equal.

m∠8  =  m∠4

m∠8  =  75°

Problem 2 :

In the figure shown below, m∠2 = 78°. Find the measures of ∠6, ∠10 and ∠14.

Solution : 

In the figure above, lines m and n are parallel, p and q are parallel.

∠2 and ∠6 are corresponding angles and they are equal. 

m∠6  =  m∠2

Substitute m∠2 = 78°.

m∠6  =  78°

∠6 and ∠14 are corresponding angles and they are equal. 

m∠14  =  m∠6

Substitute m∠6 = 78°.

m∠14  =  78°

∠10 and ∠14 are corresponding angles and they are equal. 

m∠10  =  m∠14

Substitute m∠14 = 78°.

m∠10  =  78°

Therefore, 

m∠6  =  78°

m∠10  =  78°

m∠14  =  78°

Problem 3 :

In the figure shown below, lines m and n are parallel and p is transversal. Find the value of x. 

Solution :

In the figure above m and n are parallel and p is transversal. Angles 5x° and (3x + 28)° are corresponding angles and they are equal. 

5x°  =  (3x + 28)°

5x  =  3x + 28

Subtract 3x from each side. 

2x  =  28

Divide each side by 2.

x  =  14

Problem 4 :

In the figure shown below, solve for x. 

Solution :

In the figure above, two parallel lines are intersected by another two parallel lines.

y° and 106° are corresponding angles and they are equal.

y°  =  106°

(4x + 6)° and y° are corresponding angles and they are equal.

(4x + 6)°  =  y°

Substitute y° = 106°.

(4x + 6)°  =  106°

4x + 6  =  106

Subtract 6 from each side. 

4x  =  100

Divide each side by 4.

x  =  25

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