It seems like you're asking for a counterexample to the statement "If the measures of ∠P, ∠Q, and ∠R sum to 180°, then all of the angles must be acute."

A counterexample is a specific case that disproves a statement or proposition. In this case, we need to find angles P, Q, and R that sum to 180° but are not all acute.

An acute angle is an angle less than 90°. So, if any of the angles P, Q, or R is 90° or more, it would serve as a counterexample.

For instance, let's say:
m∠P = 90°,
m∠Q = 60°,
m∠R = 30°

The sum of these angles is 180°, but not all of them are acute because ∠P is a right angle, not an acute angle. Therefore, this is a counterexample to the statement.

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It seems like you're asking for a counterexample to the statement "If the measures of ∠P, ∠Q, and ∠R sum to 180°, then all of the angles must be acute."

A counterexample is a specific case that disproves a statement or proposition. In this case, we need to find angles P, Q, and R that sum to 180° but are not all acute.

An acute angle is an angle less than 90°. So, if any of the angles P, Q, or R is 90° or more, it would serve as a counterexample.

For instance, let's say:
m∠P = 90°, 
m∠Q = 60°, 
m∠R = 30°

The sum of these angles is 180°, but not all of them are acute because ∠P is a right angle, not an acute angle. Therefore, this is a counterexample to the statement.

Knowee AI · Accepted Answer

It seems like you're asking for a counterexample to the statement "If the measures of ∠P, ∠Q, and ∠R sum to 180°, then all of the angles must be acute."

A counterexample is a specific case that disproves a statement or proposition. In this case, we need to find angles P, Q, and R that sum to 180° but are not all acute.

An acute angle is an angle less than 90°. So, if any of the angles P, Q, or R is 90° or more, it would serve as a counterexample.

For instance, let's say:
m∠P = 90°, 
m∠Q = 60°, 
m∠R = 30°

The sum of these angles is 180°, but not all of them are acute because ∠P is a right angle, not an acute angle. Therefore, this is a counterexample to the statement.

(a)If the measures of ∠P, ∠Q, and ∠R sum to 180°, then all of the angles must be acute.=Counterexample:m∠P=, °m∠Q=, °m∠R°

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