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# Define Adjacent angles, Linear pair of angles. What is the sum of a linear pair of angles?

Last updated date: 18th Sep 2024
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Hint: We start the problem by explaining what are adjacent angles, types of adjacent angles and properties of them. We then give examples which support the adjacent angles conditions. Similarly, we define what a linear pair of angles are and properties of them. We then prove the sum of the linear pair of angles as ${{180}^{\circ }}$ by taking an example which clearly depicts a linear pair of angles.

Adjacent Angles: The two angles are said to be adjacent angles when they share the common vertex and side. The endpoints of the ray from the side of an angle is called the vertex of the angle. Adjacent angles can be a complementary angle (which sum up to ${{90}^{\circ }}$) or supplementary angle (which sum up to ${{180}^{\circ }}$) when they share the common vertex and side.
Linear pair of angles is actually a special form of adjacent angles where only one condition is necessary that if sum up to ${{180}^{\circ }}$.
$\angle AOB+\angle BOC\ =\ {{180}^{\circ }}$ so here, $\angle AOB$ and $\angle BOC$ is adjacent as well as linear pair as their sum adds up to ${{180}^{\circ }}$.