Question

determine whether the conditional and its converse are both true. if both are true, combine them as a biconditional. if either is false, give a counterexample.if an angle is a right angle, its measure is 90.if an angle measure is 90, the angle is a right angle.
one statement is false. if an angle measure is 90, the angle may be a vertical angle.
one statement is false. if an angle is a right angle, its measure may be 180.
both statements are true. an angle is a right angle if (and only if) its measure is 90.
both statements are true. the measure of angle is 90 if (and only if) it is not a right angle.

Explanation:

Step1: Analyze the conditional statement

The conditional statement "If an angle is a right - angle, its measure is 90" is true by the definition of a right - angle.

Step2: Analyze the converse statement

The converse "If an angle measure is 90, the angle is a right - angle" is also true by the definition of a right - angle.

Step3: Form the biconditional

Since both the conditional and its converse are true, we can form a biconditional. A biconditional statement combines the conditional and its converse. The biconditional is "An angle is a right - angle if and only if its measure is 90".

Answer:

C. Both statements are true. An angle is a right angle if (and only if) its measure is 90.