Question

which angles are complementary to each other? ∠3 and ∠2 ∠3 and ∠4 ∠4 and ∠5 ∠2 and ∠6

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles are defined as two angles whose sum is \(90^{\circ}\).

Step2: Analyze \(\angle3\) and \(\angle2\)

\(\angle3 = 90^{\circ}\), \(\angle2+\angle3\): We know that \(\angle2+\angle3
eq90^{\circ}\) (since \(\angle3 = 90^{\circ}\) and \(\angle2>0^{\circ}\)).

Step3: Analyze \(\angle3\) and \(\angle4\)

\(\angle3 = 90^{\circ}\), \(\angle3+\angle4
eq90^{\circ}\) (since \(\angle4>0^{\circ}\)).

Step4: Analyze \(\angle4\) and \(\angle5\)

We know that \(\angle4+\angle5
eq90^{\circ}\) (they are adjacent and form a linear - pair with another angle, and their sum is not \(90^{\circ}\)).

Step5: Analyze \(\angle2\) and \(\angle6\)

We know that \(\angle1+\angle2+\angle3 = 180^{\circ}\) (straight - line angle), \(\angle3 = 90^{\circ}\), so \(\angle1+\angle2=90^{\circ}\). Also, \(\angle1=\angle6\) (vertically - opposite angles). By substitution, \(\angle6+\angle2 = 90^{\circ}\).

Answer:

\(\angle2\) and \(\angle6\)