Question

Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.

Statement Reason
Points A, B, and C form a triangle. given
Let be a line passing through B and parallel to . definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4
m∠1 = m∠4 and m∠3 = m∠5
m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180° substitution

Answer 1

Answer:

Step-by-step explanation:

The sum of angles of a triangle will always give 180°.

It cannot give less than this or more than these.

Supplementary angles also add up to 180°.

That is to say if x and y are supplementary then :

x + y = 180°

So given the shape ABC and given that it forms a triangle then the sum of the angles will give us 180°.

The statement is thus correct and true.

Answer 2

Given that.

A, B, and C form a triangle.

The sum of the interior angles of ΔABC is 180°.

We need to find the complete the statements to prove that the sum of the interior angles of ΔABC is 180°

Using diagram,

We have a triangle ABC with angle 1,2 and 3.

line DE and AC are parallel and BA is traversal line.

According to figure,

The alternate interior angle is

$\angle 1 =\angle 4$

$\angle 3=\angle 5$

So, The angle formed on line is

$\angle 4+\angle 2+\angle 5=180$

$\angle 1+\angle 2+\angle 3=180$

So, The alternate interior angle is

$\angle 1=\angle 4$

$\angle 3=\angle 5$

Hence, (3) is correct statement.