Question

#18 if two angles are complementary, both angles are acute.
choose
if the statement above is false, provide a counter - example.
your answer
#19 the product of any integer and 10, ends in a 0.
choose
if the statement above is false, provide a counter - example.
your answer

Explanation:

1. Analyze the first - statement about complementary angles

Complementary angles are two angles whose sum is 90 degrees. An acute angle is an angle whose measure is between 0 and 90 degrees. If one angle is 90 degrees and the other is 0 degrees, they are complementary but 90 - degree angle is not acute. So the statement "If two angles are complementary, both angles are acute" is false.

2. Provide counter - example for complementary angles

A counter - example is an angle of 90 degrees and an angle of 0 degrees. Their sum is 90 degrees (90 + 0=90), so they are complementary, but the 90 - degree angle is a right angle, not an acute angle.

3. Analyze the second statement about the product of an integer and 10

Let \(n\) be an integer. We can write \(n\) in the form \(n=a_{k}10^{k}+a_{k - 1}10^{k - 1}+\cdots+a_{1}10 + a_{0}\), where \(0\leq a_{i}\leq9\) and \(a_{k}
eq0\). Then \(n\times10=(a_{k}10^{k}+a_{k - 1}10^{k - 1}+\cdots+a_{1}10 + a_{0})\times10=a_{k}10^{k + 1}+a_{k - 1}10^{k}+\cdots+a_{1}10^{2}+a_{0}10\). So the product of any integer and 10 ends in 0. The statement "The product of any integer and 10 ends in 0" is true.

Answer:

1. False; Counter - example: 90 - degree and 0 - degree angles
2. True; No counter - example (since the statement is true)