Question

which angles are complementary to each other?
∠4 and ∠5 ∠4 and ∠1 ∠1 and ∠3 ∠4 and ∠2

Explanation:

Step1: Recall the definition of complementary angles

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

Step2: Analyze each pair

• For \(\angle4\) and \(\angle5\):

Since \(\angle1 = 90^{\circ}\), and \(\angle2+\angle3+\angle4+\angle5 = 180^{\circ}-\angle1=90^{\circ}\). But from the figure, we can see that \(\angle4+\angle5\) forms a right - angle adjacent part. In fact, \(\angle4+\angle5 = 90^{\circ}\) (because of the right - angle structure in the figure).

• For \(\angle4\) and \(\angle1\): \(\angle4+\angle1

eq90^{\circ}\) (as \(\angle1 = 90^{\circ}\) and \(\angle4>0^{\circ}\)).

• For \(\angle1\) and \(\angle3\): \(\angle1+\angle3

eq90^{\circ}\) (since \(\angle1 = 90^{\circ}\) and \(\angle3>0^{\circ}\)).

• For \(\angle4\) and \(\angle2\): \(\angle4+\angle2

eq90^{\circ}\) (by observing the angle measures in the figure).

Answer:

\(\angle4\) and \(\angle5\)