Question

A line through point A is drawn parallel to the base of ABC. Without using a protractor, justify that the three angles of ABC add up to 180 degrees.

Answer 1

see explanation

Explanation:

Since the line through A is parallel to BC, then

b = 3 ( alternate angles )

a = 1 ( alternate angles )

a + 2 + b = 180° ( straight angle ), thus

1 + 2 + 3 = 180°

Thus the 3 angles of ΔABC sum to 180°