Question

use the conditional statement to answer the question. if an angle measures 43°, then the angle is acute. are the statement and its inverse true? the statement is true, but the inverse is false. the statement is false, but the inverse is true. both the statement and its inverse are true. both the statement and its inverse are false.

Explanation:

Step1: Define an acute - angle

An acute - angle is an angle whose measure is between 0° and 90°. Since 43° is between 0° and 90°, the statement "If an angle measures 43°, then the angle is acute" is true.

Step2: Write the inverse of the conditional statement

The inverse of the conditional statement "If p, then q" is "If not p, then not q". The original statement is "If an angle measures 43°, then the angle is acute". Its inverse is "If an angle does not measure 43°, then the angle is not acute". An angle that is not 43° can still be acute (e.g., 30°), so the inverse is false.

Answer:

The statement is true, but the inverse is false.