**Exterior angles and remote interior angles worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on exterior angle and its two remote interior angles in a triangle.

**1. Sketch a triangle and label the exterior angle and its two remote interior angles. **

**2. Find the **relationship between the measure of an exterior angle and the measures of its remote interior angles.

3. How many exterior angles does a triangle have at each vertex ?

4. How many total exterior angles does a triangle have ?

**Problem 1 : **

**Sketch a triangle and label the exterior angle and its two remote interior angles. **

**Solution : **

In the above diagram,

- m∠1, m∠2, and m∠3 are interior angles.
- m∠4 is an exterior angle.
- m∠1 and m∠2 are remote interior angles to m∠4.

**Problem 2 :**

**Find the **relationship between the measure of an exterior angle and the measures of its remote interior angles.

**Solution : **

There is a special relationship between the measure of an exterior angle and the measures of its remote interior angles.

Let us understand this relationship through the following steps.

**Step 1 :**

**Sketch a triangle and label the angles as **m∠1, m∠2 and m∠3.

**Step 2 :**

According to Triangle Sum Theorem, we have

m∠1 + m∠2 + m∠3 = 180° ------ (1)

**Step 3 :**

Extend the base of the triangle and label the exterior angle as m∠4.

**Step 4 :**

m∠3 and m∠4 are the angles on a straight line.

So, we have

m∠3 + m∠4 = 180° ------ (2)

**Step 5 :**

Use the equations (1) and (2) to complete the following equation,

m∠1 + m∠2 + m∠3 = m∠3 + m∠4 ------ (3)

**Step 6 :**

Use properties of equality to simplify the equation (3).

m∠1 + m∠2 + m∠3 = m∠3 + m∠4

Subtract m∠3 from both sides.

aaaaaaaaaaa m∠1 + m∠2 + m∠3 = m∠3 + m∠4 aaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa - m∠3 - m∠3 aaaaaaaaaaaaaaaaa aaaaaaaaaaa ------------------------------------ aaaaaaaaaaa aaaaaaaaaaa m∠1 + m∠2 = m∠4 aaaaaaaaaaa aaaaaaaaaaa ------------------------------------ aaaaaaaaaaa

Hence, the Exterior Angle Theorem states that the measure of an** exterior** angle is equal to the sum of its **remote interior** angles.

**Problem 3 : **

How many exterior angles does a triangle have at each vertex ?

**Solution : **

Sketch a triangle and draw all of its exterior angles.

From the diagram given above, it is clear that each vertex has **two** exterior angles.

**Problem 4 : **

How many total exterior angles does a triangle have ?

**Solution : **

**From the diagram given in the above problem 3, it is clear that ** a triangle has a total of **six** exterior angles.

After having gone through the stuff given above, we hope that the students would have understood "Exterior angles and remote interior angles worksheet".

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