Question

determine whether the statement can be assumed from the given figure. explain.

∠6 and ∠8 are complementary.

select choice because ∠7 is a(n) select choice, ∠6 and ∠8 must form a(n) select choice.

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Explanation:

Step1: Recall the definition of complementary angles

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

Step2: Analyze the relationship of angles in the figure

In the figure, since \(\angle7 = 90^{\circ}\) (right - angle symbol), and \(\angle6+\angle7+\angle8 = 180^{\circ}\) (straight - angle). Substitute \(\angle7 = 90^{\circ}\) into \(\angle6+\angle7+\angle8 = 180^{\circ}\), we get \(\angle6+\angle8=180^{\circ}-\angle7\).

Step3: Calculate \(\angle6+\angle8\)

Substitute \(\angle7 = 90^{\circ}\) into \(\angle6+\angle8=180^{\circ}-\angle7\), then \(\angle6+\angle8 = 180^{\circ}-90^{\circ}=90^{\circ}\)

Answer:

Yes; right - angle; right - angle. \(\angle6\) and \(\angle8\) are complementary because \(\angle6+\angle8 = 90^{\circ}\) (since \(\angle6+\angle7+\angle8=180^{\circ}\) and \(\angle7 = 90^{\circ}\))