In GMAT exam, the sums of Angles are the most interesting ones as solving them includes lots of shortcuts. You can learn more on GMAT Quant Shortcut Techniques right here.

Most of the bases of fundamental geometry facts are made from the properties of parallel and perpendicular lines. These include the facts about which angles are equal when lines intersect and how to get the various values if the lines are parallel in nature. The most special properties of the parallel lines directly connected to the most famous theorem of Geometry known as the 180°-Triangle Theorem:

**What is the 180°-Triangle Theorem?**

According to this theorem, the sum of all the interior angles of a triangle is equal to 180°. This is a true fact, irrespective of the fact that what kind of triangle we are dealing with.

**Relations between Angles and Lines**

When two parallel lines are intersected by a third line, then all the angles hold some relation with one another. Let’s look at these relationships.

In this figure, two parallel lines are being traversed by a traversal line.

So, Angles, 1, 3, 6 and 8 is equal

Whereas, angles, 2, 4, 5 and 7 are equal.

As well, sum of any two adjacent angles is equal to 180°.

Let’s solve a problem and explain it in further details.

In the above diagram, if angle b = angle c.

Then which of the following is not true?

- a = c
- b= d
- e= f
- f= h
- none of the above

Solution:

As given in the question that the lines are parallel, we know that from properties of parallel lines,

a= b

c = d

e = f

g = h

Given that

b = c

So, a= b = c = d

But there is no relation given between f and h. So, it is not true.

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