**What are the corresponding angles?**

**What are the corresponding angles?**

When a third line intersected two parallel lines, the angle made by the same relative position at each intersection is called the corresponding angle to each other.

When a line known as intersecting traversal crosses a pair of straight lines, corresponding angles are formed. Corresponding angles are the pair of angles formed on a different intersection in the same relative position. Here \theta is the Corresponding angle.

**To understand corresponding angles some important terms must be understood.**

## Intersection of Lines

**An intersecting line is formed by two or more lines crossing one another and forming multiple angles at the vertex. Whenever two lines touch or cross, they are said to be intersecting.**

## Parallel lines

A parallel line is unique in that it cannot touch or intersect with any other line, regardless of how long it extends for. They always remain the same distance apart. Corresponding angles can be used to check whether two lines are parallel.

## Transversal Line

An intersection or crossing of parallel lines is called a transversal.

**Types of Corresponding Angles**

There are **two** types of corresponding angles.

- Corresponding angles formed by parallel lines and transversals
- Corresponding angles formed by non-parallel lines and transversals

## Corresponding Angles formed by Parallel Lines and Transversals

If a line or a transversal crosses two parallel lines, then the corresponding angles are equal. According to the given figure, two parallel lines are intersected by a transversal, which form 8 angles. As a result, the angles formed by the first and second lines with transversals are equal.

## Real-life Examples of corresponding Angles

Corresponding angles are pairs of angles that occupy the same relative position at the intersection of two lines and are on the same side of the transversal. In real-life scenarios, corresponding angles can be found in various contexts such as architecture, engineering, and everyday objects. Here are some examples:

**City Street Grids**: In urban planning, city street grids often intersect at right angles. When streets cross each other, the angles formed by the intersections are corresponding angles. For instance, if you look at the intersection of two perpendicular streets, the angles formed by each pair of opposite corners are corresponding angles.

**Window Panes**: The framework of a window often forms a grid-like pattern. When two windows are placed adjacent to each other, the diagonal bars within the window frames form corresponding angles where they intersect.

**Railway Tracks**: At railway crossings, the tracks often form intersecting lines. The angles formed by the intersection of the tracks are corresponding angles.

**Lattice Structures**: In architecture and engineering, lattice structures such as bridges and towers often have diagonal supports that intersect. The angles formed by these intersecting supports are corresponding angles.

**Fences and Gates**: Many fences and gates have intersecting bars or slats. The angles formed by the intersection of these bars or slats are corresponding angles.

**X-shaped Supports**: In furniture or architectural design, X-shaped supports or braces are common. The angles formed where the supports intersect are corresponding angles.

## Questions and their solution about Corresponding Angles

**Question:** In a figure where two parallel lines are intersected by a transversal, angle C is 75 degrees. Angle C is positioned at the lower right of the intersection on one parallel line. Find the measure of the corresponding angle on the other parallel line, which is situated at the upper right of the intersection when looking from the same side as angle C.

**Solution:** Since corresponding angles are equal and angle C is given as 75 degrees, the corresponding angle on the other parallel line, situated at the upper right of the intersection, will also be 75 degrees. This is based on the property that corresponding angles formed by a transversal with two parallel lines are always equal.

To provide a clear visual representation of this solution, let’s generate an image depicting this scenario, showing the parallel lines, the transversal, angle C, and its corresponding angle, both marked as 75 degrees.

In the provided example, we illustrated a scenario with two parallel lines intersected by a transversal. We labeled angle C as 75 degrees, positioned at the lower right of the intersection on one of the parallel lines. The corresponding angle on the other parallel line, situated at the upper right of the intersection, is also marked as 75 degrees. This visual representation demonstrates the principle that corresponding angles between parallel lines are equal, effectively solving the posed question.