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The given statement m∠1 = m∠4 and m∠3 = m∠5, its reason is Alternate Interior Angle.
<u>Step-by-step explanation:</u>
Let ABC is a triangle and a line DE traverses through the point B.
That results in AC is parallel to DE.
From the diagram, m∠1 and m∠4 is alternate to each other and m∠3 and m∠5 is alternate to each other. Also, they present in the interior position.
According to alternate interior theorem, when a line traverses through two parallel line creates equal angles in the interior sides which the angles will be opposite to each other.
⇒ m∠1 = m∠4 and m∠3 = m∠5. (refer the diagram).
Now let us continue with the proof,
The total angle of the straight line is 180°.
Here the straight line is DE which consists of three angles m∠4, m∠2, m∠5.
⇒m∠4 + m∠2 + m∠5 = 180° .
we know that, m∠1 = m∠4 and m∠3 = m∠5.
Let us substitute in the above equation.
m∠1 + m∠2 + m∠3 = 180°.
Hence proved.
