Question

for which conditions does the statement have a truth value of false? if the measure of angle abc is 95°, then triangle abc is an obtuse triangle. the measure of angle abc is 95° and triangle abc is an obtuse triangle. the measure of angle abc is not 95° and triangle abc is an obtuse triangle. the measure of angle abc is 95° and triangle abc is not an obtuse triangle. the measure of angle abc is not 95° and triangle abc is not an obtuse triangle.

Explanation:

Step1: Recall the truth - value of a conditional statement

A conditional statement \(p
ightarrow q\) (if \(p\), then \(q\)) is false when \(p\) is true and \(q\) is false.

Let \(p\) be “the measure of angle \(ABC\) is \(95^{\circ}\)” and \(q\) be “Triangle \(ABC\) is an obtuse triangle”.

Step2: Analyze each option

• Option 1: \(p = \text{True}\), \(q=\text{True}\). For \(p

ightarrow q\), when \(p\) is True and \(q\) is True, \(p
ightarrow q\) is True.

• Option 2: \(p=\text{False}\), \(q = \text{True}\). For \(p

ightarrow q\), when \(p\) is False and \(q\) is True, \(p
ightarrow q\) is True.

• Option 3: \(p=\text{True}\), \(q=\text{False}\). For \(p

ightarrow q\), when \(p\) is True and \(q\) is False, \(p
ightarrow q\) is False.

• Option 4: \(p=\text{False}\), \(q=\text{False}\). For \(p

ightarrow q\), when \(p\) is False and \(q\) is False, \(p
ightarrow q\) is True.

Answer:

The measure of angle \(ABC\) is \(95^{\circ}\) and triangle \(ABC\) is not an obtuse triangle.