Question

1. (a) tell whether angle ∠gfh is an acute, right, obtuse, straight, or reflex angle.

a. acute
b. right
c. obtuse
d. straight
e. reflex

1. (a) select the venn - diagram that represents the following set of conditional statements: the sale included all head gear (items you wear on your head), sunglasses are head gear, so all sunglasses are on sale.

a. venn - diagram with sunglasses circle containing head gear circle which contains sale circle
b. venn - diagram with head gear circle containing sale circle which contains sunglasses circle
c. venn - diagram with sale circle containing sunglasses circle which contains head gear circle
d. venn - diagram with head gear circle containing sunglasses circle which contains sale circle
e. venn - diagram with sale circle containing head gear circle which contains sunglasses circle

1. (a) select the reverse of the definition below and tell whether it passes the reversibility test. a drink made with eggs and milk is eggnog.

a. eggnog is a drink made with eggs and milk; does not pass
b. the only drink made with eggs and milk is eggnog; does not pass
c. the only drink made with eggs and milk is eggnog; passes
d. eggnog is a drink made with eggs and milk; passes
e. all drinks are made with eggs and milk; does not pass

Explanation:

16.

Step1: Recall angle - type definitions

An acute angle is between \(0^{\circ}\) and \(90^{\circ}\), a right - angle is \(90^{\circ}\), an obtuse angle is between \(90^{\circ}\) and \(180^{\circ}\), a straight angle is \(180^{\circ}\), and a reflex angle is between \(180^{\circ}\) and \(360^{\circ}\).

Step2: Observe \(\angle GFH\)

The angle \(\angle GFH\) is between \(90^{\circ}\) and \(180^{\circ}\).

Step1: Analyze the set - relationship

The sale includes all head - gear, and sunglasses are a subset of head - gear. So, the set of sunglasses is a subset of the set of head - gear, and the set of head - gear is a subset of the set of items on sale.

Step2: Match with Venn - diagrams

The correct Venn - diagram should have a large circle for "Sale", a smaller circle inside it for "Head gear", and an even smaller circle inside "Head gear" for "Sunglasses".

Step1: Find the reverse of the definition

The original statement is "A drink made with eggs and milk is eggnog." The reverse is "The only drink made with eggs and milk is eggnog."

Step2: Check reversibility

For a definition to pass the reversibility test, the original and the reverse statements must both be true. Since eggnog is defined as a drink made with eggs and milk and if we assume that there are no other drinks made with just eggs and milk, the reverse statement is true.

Answer:

C. obtuse

17.