Question

show that in any triangle sum of its interior angle is 180​

Answer 1

Step-by-step explanation:

Let's take a triangle say ABC, with interior angles as P, Q and R.

Now construct a line parallel to the base AB of triangle as shown in the attachment.

Since AB is parallel to the constructed line, by alternate interior angle property we get,

$\rm\to\:\angle\:n\:=\:\angle\;Q$

$\rm\to\:\angle\:m\:=\:\angle\;P$

We know that angles created by line segments on a straight line is 180°.

By this we get,

$\rm\longrightarrow \:\angle \:n \:+\angle\:m\:+\:\angle\:R=180^{\circ}$

Replace angle n with Q and m with P as we have discussed about it above.

$\rm\longrightarrow \:\angle \:Q \:+\angle\:P\:+\:\angle\:R=180^{\circ}$

Hence this is proved that sum of all interior angles of a triangle is 180°.