Interior & Exterior Angles of Triangles

Question 1

The angle sum theorem states…?

Answer 1

the three interior angles of any triangle add up to 180 degrees.

Question 2

The exterior angle theorem states…?

Answer 2

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Question 3

The picture shows what theorem? Angle sum theorem or exterior angle theorem?

Answer 3

The Angle Sum Theorem

Question 4

The picture shows what theorem? Angle sum theorem or exterior angle theorem?

Answer 4

The Exterior Angle Theorem

Question 5

Given the measure of two interior angles of a triangle, how do you find the third interior angle?

Answer 5

Since the angle sum theorem tells us all three interior angles add to 180, we would subtract the two given angles from 180 to find the third interior angle.

Question 6

Find the missing angle of the triangle in the picture.

Answer 6

71

Question 7

Find the missing angle of the triangle in the picture.

Answer 7

36

Question 8

Find the missing angle of the triangle in the picture.

Answer 8

80

Question 9

Find the missing angle of the triangle in the picture.

Answer 9

105

Question 10

How would you set up the equation to solve for x in the given picture?

Answer 10

You would take each of the expressions given in the triangle and add them together then make all of them equal 180. Like this: 3x+2+2x+12+x=180

Question 11

How can you find an exterior angle if you know the measure of the two interior angles opposite from it?

Answer 11

You could add the two interior angles that are opposite from the exterior angle, and that would be what the exterior angle equals.

Question 12

How can you find one of the opposite interior angles from the exterior angle, if you know one of the interior angles and the exterior angle? For example, look at the picture.

Answer 12

You would subtract the one interior angle you know from the measure of the exterior angle to find the other interior angle.

Question 13

Find the missing angle of the triangle in the picture.

Answer 13

103

Question 14

Find the missing angle of the triangle in the picture.

Answer 14

105

Question 15

Find the missing angle of the triangle in the picture.

Answer 15

52

Question 16

Find the missing angle of the triangle in the picture.

Answer 16

69

Question 17

How would you set up the equation to solve for x in the given picture?

Answer 17

You would add both of the expressions that represent the interior angles and make them equal to the expression of the exterior angle. Like this: -3x-4+7x=70+2x