Question

which angles are complementary to each other?
∠6 and ∠3 ∠2 and ∠3 ∠4 and ∠3 ∠2 and ∠4
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not feeling ready yet? these can help:
angle vocabulary
lesson: complementary angle
lesson: supplementary angles
lesson: vertical angles
lesson: adjacent angles

Explanation:

Step1: Recall the definition of complementary angles

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

Step2: Analyze each pair of angles

• For \(\angle6\) and \(\angle3\): There is no information to suggest their sum is \(90^{\circ}\).
• For \(\angle2\) and \(\angle3\): Given that \(\angle3 = 90^{\circ}\), \(\angle2+\angle3

eq90^{\circ}\)

• For \(\angle4\) and \(\angle3\): \(\angle4+\angle3

eq90^{\circ}\)

• For \(\angle2\) and \(\angle4\): Since \(\angle4+\angle5+\angle6 = 180^{\circ}\) (straight - line angle), \(\angle1+\angle2+\angle3 = 180^{\circ}\) (straight - line angle), \(\angle3 = 90^{\circ}\), and \(\angle4=\angle1\) (vertical angles). Then \(\angle2+\angle4=\angle2 + \angle1=90^{\circ}\) (because \(\angle3 = 90^{\circ}\) and \(\angle1+\angle2+\angle3=180^{\circ}\), so \(\angle1+\angle2=90^{\circ}\))

Answer:

\(\angle2\) and \(\angle4\)