(b)If ∠1 and ∠2 are complementary angles, then one of them must have a measure greater than 45°.=Counterexample:m∠1=, °m∠2°

If ∠1 and ∠2 are complementary angles, then one of them must have a measure greater than 45°.

(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°

Show that each statement is false by providing a counterexample.(a)If the length of AC is 46 and point B lies on AC, then =AB34 and =BC12.=Counterexample:AB=, BC(b)If the perimeter of a rectangle is 12, then the length is 3 and the width is 3.=Counterexample:length=, width(c)If ∠1 and ∠2 are complementary angles, then one of them must have a measure less than 45°.=Counterexample:m∠1=, °m∠2°(d)If the measures of ∠R, ∠S, and ∠T sum to 180°, then one of the angles must be obtuse.=Counterexample:m∠R=, °m∠S=, °m∠T°

In △𝐴𝐵𝐶, 𝐴𝐵=6𝑐𝑚, 𝐴𝐶=12𝑐𝑚, 𝑚∠𝐴=60∘ and  𝐴𝐶― is the longest side. Which of the following statements about the measures of the angles in △𝐴𝐵𝐶 must be true? (Note: 𝑚∠𝑋 denotes the measure of angle X.)

Select all the correct answers.If the measure of angle is 𝜃  is 7⁢𝜋4 , which statements are true? The measure of the reference angle is 60∘ . The measure of the reference angle is 30∘ . sin(𝜃)=-22 The measure of the reference angle is 45∘ . cos(𝜃)=-22 tan(𝜃)=-1