Question

prove that the opposite angles formed by two intersecting lines are of equal measures​

Answer 1

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Answer 2

Step-by-step explanation:

Given:

$AB$ and $CD$ are intersecting lines.

$O$ is the point of intersection.

To prove: $x=y$ and $p=q$

Proof:

From the figure, $AB$ and $CD$ intersect at point $O$.

From straight line rule:

$x$ and $q$ are linear pair angle which means $x+q=180^{o}$

Also, $y$ and $q$ are linear pairs which means $y+q=180^{o}$

From both the above equations, using elimination method:

$x=y$

Similarly, $p=q$

Hence, vertically opposite angles are equal when two lines intersect each other.