LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

VERTICALLY OPPOSITE ANGLE

__VERTICALLY OPPOSITE ANGLE -__

**When two straight lines intersect each other, they form four angles at their point of intersection say a, b, c, and d.**

**Angles a & c are called vertically opposite angles to each other and so are angles b & d.**

**They are called vertically opposite angles because they have the same vertex and are opposite to each other.**

__Properties Of Vertically Opposite Angles -__

**(i) The adjacent angles are supplementary angles.**

**As angles a & b are on a straight line,**

**So, ∠a + ∠b = 180⁰ **

**Hence, angles a & b are supplementary angles.**

**Similarly, angles b & c, angles c & d, angles a & d, are supplementary angles. **

**(ii) Vertically opposite angles are equal.**

**As a & b are on a straight line So, ∠a + ∠b = 180⁰ ...............(1)**

**Also, as angles b & c are on a straight line.**

**So, ∠b + ∠c = 180⁰ ...............(2)**

**From (1) & (2), we get -**

**∠a + ∠b = ∠b + ∠c**

**=> ∠a = ∠c**

**In the same way, we can show that ∠b = ∠d**