Ancient mathematicians presented the concept of lines to represent straight objects which had negligible width and also depth. Considered as a breadth less size by Euclid, lines type the basis of Euclidean geometry.

You are watching: An angle is formed by a vertex and a line

When two rays (part of a right line) crossing each various other in the very same plane, they form an angle. The point of intersection is called a vertex.

In this article, we go over the straightforward properties, definitions, and varieties of lines and also angles concerned geometry. We’ll likewise look at a few examples because that you to know the nature of lines and angles in a better manner. Before we relocate forward, take a look at the five-step GMAT Preparation plan to score 700+ on the GMAT:


complying with is a brief outline of the topics the we will certainly cover in this article

Application that Lines and Angles properties in Questions

Definition the Line

A line does no have any type of endpoints. It has actually an infinite length.

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In the diagram provided above, the line CD is parallel to line EF. If ∠AHD and also ∠JIE space 118° and 30° respectively, then what is the measure up of edge GIB?

3032344062Solution

Step 1: Given

line CD is parallel to line EF.∠AHD =118°∠JIE = 30°

Step 2: come find

Measure of edge ∠GIB

Step 3: Approach and Working out


We require to find the measure up of edge GIB.

So, v the offered information, we understand that heat CD is parallel to heat EF and line abdominal is transversal to them.Hence, ∠DHI = ∠FIB together both are equivalent angles.We can discover ∠DHI or ∠FIB as∠AHD + ∠DHI = 180°118°+ ∠FIB = 180°∠FIB = 62°Now, ∠FIB = ∠FIG + ∠GIBBy observing the diagram, ∠FIG = ∠JIE together these space vertically the opposite angles in between EF and also JG.∠FIB = ∠FIG + ∠GIB62°= ∠JIE + ∠GIB62°= 30°+ ∠GIB∠GIB = 32°

Hence, the exactly answer is choice B.

Lines and also Angles – concern 2


In the diagram provided above, edge DFE and angle BFC are stood for by X and also Y respectively. If ∠AFC = 100° and also ∠BFE = 45°then what is the value of Y-X?

2025303540Solution

Step 1: Given

∠DFE = X∠BFC = Y∠AFC = 100°∠BFE = 45°

Step 2: to find

The value of Y-X

Step 3: Approach and also Working out

To find Y-X, we need to uncover Y and also X first.

Measure of angle Y:

We are offered ∠AFC = 100°and,∠AFC + ∠BFC = 180°as the sum of angle on the same side directly line is 180°100°+ ∠BFC = 180°∠BFC = Y = 80°

Measure of edge X:

We are offered ∠BFE = 45°and,∠DFE + ∠BFE + ∠BFC = 180°as the sum of angle on the same side directly line is 180°.X + 45°+80°= 180°X = 55°

Hence, Y – X = 80°– 55°=25°.

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Thus, the correct answer is choice B.

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