Question

problem 21: select the converse of this statement, and determine whether it is true or false. if two angles are supplementary, then the sum of the measures of their angles is 180.

Explanation:

Step1: Recall converse definition

The converse of a conditional statement "If p, then q" is "If q, then p". Here, p = "two angles are supplementary" and q = "the sum of the measures of their angles is 180".

Step2: Form the converse

By swapping p and q, we get "If the sum of the measures of two angles is 180, then the two angles are supplementary".

Step3: Determine truth - value

By the definition of supplementary angles (two angles are supplementary if and only if the sum of their measures is 180), the converse is true.

Answer:

The converse statement: If the sum of the measures of two angles is 180, then the two angles are supplementary. It is true.