EXTERIOR ANGLE AND REMOTE INTERIOR ANGLES WORKSHEET

Problem 1 :

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

Problem 2 :

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

Problem 3 :

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

Problem 4 :

How many total exterior angles does a triangle have?

Answers

1. Answer :

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.
  

2. Answer :

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.

m∠1 + m∠2  =  m∠4

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

3. Answer :

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.

4. Answer :

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

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