Ancient mathematicians introduced the concept of lines to represent straight objects which had negligible width and depth. Considered as a breadth less length by Euclid, lines form the basis of Euclidean geometry.
Đang xem: Geometry lines and angles
When two rays (part of a straight line) intersect each other in the same plane, they form an angle. The point of intersection is called a vertex.
In this article, we go over the basic properties, definitions, and types of lines and angles related to geometry. We’ll also look at a few examples for you to understand the properties of lines and angles in a better manner.
In the diagram given above, angle DFE and angle BFC are represented by X and Y respectively. If ∠AFC = 100° and ∠BFE = 45° then what is the value of Y-X?
Step 1: Given
∠DFE = X∠BFC = Y∠AFC = 100°∠BFE = 45°
Step 2: To find
The value of Y-X
Step 3: Approach and Working out
To find Y-X, we need to find Y and X first.
Measure of angle Y:
We are given ∠AFC = 100° and,∠AFC + ∠BFC = 180° as the sum of angles on the same side straight line is 180°100° + ∠BFC = 180°∠BFC = Y = 80°
Measure of angle X:
We are given ∠BFE = 45° and,∠DFE + ∠BFE + ∠BFC = 180° as the sum of angles on the same side straight line is 180°.X + 45° +80° = 180°X = 55°
Hence, Y – X = 80° – 55° =25°.