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 .

Explanation:

Step1: Analyze ∠7's type

From the figure, ∠7 has a right - angle symbol, so ∠7 is a right angle (measures \(90^{\circ}\)).

Step2: Analyze ∠6, ∠7, ∠8 relationship

∠6, ∠7, and ∠8 are angles on a straight line (linear pair - related or forming a straight angle which is \(180^{\circ}\)). Since ∠7 = \(90^{\circ}\), then ∠6+\(90^{\circ}\)+∠8 = \(180^{\circ}\), so ∠6 + ∠8=\(90^{\circ}\).

Step3: Determine if complementary

Complementary angles are two angles whose sum is \(90^{\circ}\). Since ∠6 + ∠8=\(90^{\circ}\), ∠6 and ∠8 are complementary. Also, ∠7 is a right angle, and ∠6, ∠7, ∠8 form a straight angle (or a linear - related set where their sum is \(180^{\circ}\)).

Answer:

First "Select Choice": Yes; Second "Select Choice": right angle; Third "Select Choice": angle with ∠7 that sums to \(180^{\circ}\) (or straight angle - related) and since ∠7 is \(90^{\circ}\), ∠6 and ∠8 sum to \(90^{\circ}\) (complementary).