Question

Two angle of a triangle measure 39.5 and 61.7. Using the Triangle Angle Sum Theorem, which states that the sum of the inside angles of all triangles must equal 180, find the measure of the third angle.

68.8
68.8

78.8
78.8

88.8
88.8

98.8
98.8

Answer 1

Use the Triangle Inequality Theorem (see picture above) to solve the problem.
Two Sides of a triangle measure 11 and 3. Identify the side measure that would NOT create a triangle.

7
7

9
9

12
12

13
13

Answer 2

The measure of the third angle can be found by subtracting the sum of the two given angles from 180:

180 - (39.5 + 61.7) = 78.8

Therefore, the measure of the third angle is 78.8.

Answer 3

According to the Triangle Inequality Theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

In this case, the sides measures are 11, 3, and x.

To find the side measure that would not create a triangle, we need to check each option:

- 11 + 3 > x
- 14 > x
- x can be 7, 9, 12, or 13 for a triangle to be formed.

- 11 + x > 3
- x > -8
- x must be greater than 0.

- 3 + x > 11
- x > 8
- x can be 7, 9, 12, or 13 for a triangle to be formed.

Based on above analysis, a side measure of 7 would NOT create a triangle, as it does not satisfy the Triangle Inequality Theorem.