Question

#19: two angles that form a linear pair are always supplementary. choose if the statement above is false, provide a counterexample. your answer #20: the names of each month in a calendar year have at least 4 letters. choose if the statement above is false, provide a counterexample. your answer

Explanation:

Step1: Recall linear - pair and supplementary - angle definitions

A linear pair of angles is formed when two lines intersect. The sum of the measures of angles in a linear pair is 180 degrees. Supplementary angles are two angles whose sum of measures is 180 degrees.

Step2: Determine the truth - value of the first statement

Since the sum of angles in a linear pair is 180 degrees, two angles that form a linear pair are always supplementary. So the first statement is True.

Step3: Analyze the names of months

The months of the year are January, February, March, April, May, June, July, August, September, October, November, December. The month 'May' has 3 letters.

Step4: Determine the truth - value of the second statement

Since 'May' has 3 letters which is less than 4, the statement "The names of each month in a calendar year have at least 4 letters" is False. The counter - example is the month 'May'.

Answer:

1. True
2. False, counter - example: May