Two angles 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. (2 points) Responses 68.8° 68.8° 78.8° 78.8° 88.8° 88.8° 98.8°
The measure of the third angle can be found by adding the measures of the two given angles and subtracting the sum from 180°:
39.5° + 61.7° = 101.2°
180° - 101.2° = 78.8°
Therefore, the measure of the third angle is 78.8°.
Use the Triangle Inequality Theorem (see picture above) to solve this problem. Two sides of a triangle measure 11 and 3. Identify the side measure that would NOT create a triangle. (1 point) Responses 7 7 9 9 12 12 13
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given sides of lengths 11 and 3, let's check which side measure would NOT create a triangle:
- 7: 11 + 3 > 7 (True)
- 9: 11 + 3 > 9 (True)
- 12: 11 + 3 > 12 (True)
- 13: 11 + 3 > 13 (False)
Therefore, the side measure that would NOT create a triangle is 13.