Question

In triangle *ABC *above, side AC is extended to

point *D*. What is the value of *y-x*?

- 40
- 75
- 100
- 140

Hint:

**Hint: **

To find the value of y-x, we first need to find the value of x and y

There are two properties we need to know to find them. The sum of the interior angles of a triangle is 180.

And the exterior angle theorem which states that if a triangle's side gets extended, then the resultant exterior angle is always equal to the sum of the two opposite interior angles of the triangle.

## The correct answer is: 100

### Given, ABC is a triangle, AC is extended to point D.

Also,

Now, we know that the sum of the interior angles of a triangle is 180°.

So,

Next,

By exterior angle theorem, if a triangle's side is extended, then the resultant exterior angle is always equal to the sum of the two opposite interior angles of the triangle.

Here, AC is extended to AD. The exterior angle is The opposite angles are and

So

Thus, we get the values

Hence, the required value of

The correct option is C)

**Note: **

It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.

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