In geometry, a direct pair of angle is a pair of nearby angles developed when two lines intersect each other. Nearby angles are created when two angles have actually a usual vertex and a typical arm however do no overlap. The straight pair of angle are always supplementary as they kind on a right line. In other words, the sum of 2 angles in a linear pair is constantly 180 degrees.

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1.Definition of direct Pair that Angles
2.Properties of direct Pair of Angles
3.Linear Pair of angle Vs Supplementary Angles
4.Linear Pair Postulate

When two lines crossing each other at a solitary point, linear bag of angles space formed. If the angle so developed are surrounding to each various other after the intersection that the 2 lines, the angles are stated to it is in linear. If two angles kind a straight pair, the angles room supplementary, who measures include up come 180°. Hence, a direct pair of angle always add up to 180°.


There space some properties of straight pair of angle that make them unique and also different indigenous other varieties of angles. Look in ~ the direct pair of angle properties provided below:

The amount of two angles in a linear pair is constantly 180°.

In geometry, there are two types of angles whose amount is 180 degrees. They are direct pairs of angles and supplementary angles. We regularly say the the direct pair the angles are supplementary, but do you understand that this two species of angles room not the same? let us understand the difference between supplementary angles and also linear pair the angles with the table given below:

Linear Pair that AnglesSupplementary Angles
These angles room always nearby to every other. The means, a pair of angle whose sum is 180 degrees and they lie next to each other sharing a typical vertex and a typical arm are well-known as straight pair that angles.These angles need not it is in adjacent. Their sum is also 180°.
All direct pairs space supplementary angle too.All supplementary angles space not direct pairs.
Example: ∠1 and ∠2 in the image given below.Example: ∠A and ∠B, ∠1 and also ∠2 (in the photo below).

In the picture below, it deserve to be plainly seen that both the pairs of angles space supplementary, but ∠A and ∠B space not direct pairs due to the fact that they space not surrounding angles.


The linear pair postulate states that if a ray stands top top a line, climate the sum of two surrounding angles is 180º. Will the converse the this statement it is in true? that is if the amount of a pair of nearby angles is 180º, will certainly the non-common eight of the 2 angles form a line? Yes, the converse is likewise true. These 2 axioms are grouped with each other as the linear pair axiom. In the figure below, beam QS was standing on a heat PR forming a direct pair of angle ∠1 and ∠2.


Important Notes

In a straight pair, if the 2 angles have actually a typical vertex and also a common arm, climate the non-common side makes a right line and also the sum of the measure up of angle is 180°.Linear bag are always supplementary.

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Example 1: If among the angles forming a straight pair is a ideal angle, then what can you say about its various other angle?Solution: Let one of the angles forming a linear pair it is in 'a' and also the various other be 'b'.Given the ∠a = 90° and also we currently know that direct pairs the angles are supplementary ⇒ ∠a + ∠b = 180°.⇒ 90° + ∠b = 180°⇒ ∠b = 180° - 90°⇒ ∠b = 90°Therefore, in a linear pair that angles, if one of the angle is a ideal angle then one more angle is additionally a appropriate angle.

Example 2: In the offered figure, if POQ is a right line and ∠POC = ∠COQ, then present that ∠POC = 90°.


Since ray OC was standing on line PQ. So, by direct pair axiom, ∠POC + ∠COQ = 180°. However ∠POC = ∠COQ (given).⇒ ∠POC + ∠POC = 180°⇒ 2∠POC = 180°

⇒ ∠POC = 180°/2 = 90°⇒ ∠POC = 90°Hence Proved.

Example 3: If two angles forming a direct pair are in the proportion of 4:5, then find the measure of every of the angles.Solution: permit the 2 angles it is in 4y and also 5y.

We know that straight pair of angles room supplementary ⇒ 4y + 5y = 180°.

9y = 180°

y = 180/9

y = 20

Therefore, the 2 angles are: 4y = 4 × 20 = 80° and also 5y = 5 × 20 = 100°.

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