Question

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Answer 1

Answer:

∠3 ≅ ∠5 and ∠1 ≅ ∠4  

Alternate Interior Angles Theorem

m∠1 = m∠4 and m∠3 = m∠5  

Congruent angles have equal measures.

Step-by-step explanation:

Answer 2

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The given statement m∠1 = m∠4 and m∠3 = m∠5, its reason is Alternate Interior Angle.

Step-by-step explanation:

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.