Question

determine whether the statement can be assumed from the given figure. explain. ( mangle 5 = mangle 3 + mangle 6 ) select choice ( mangle 5 = ) select choice because it is a(n) select choice , and ( mangle 3 + mangle 6 = ) select choice because ( angle 3 ) and ( angle 6 ) are select choice angles. diagram with lines ( p ), ( t ), and angles labeled 1–8, 3, 5, 6, and arrows is present.

Explanation:

Step1: Analyze ∠5

From the figure, ∠5 has a right - angle symbol, so \(m\angle5 = 90^{\circ}\) (because it is a right angle).

Step2: Analyze ∠3 and ∠6

∠3 and ∠6 are adjacent angles that form a right angle (since the lines are perpendicular as indicated by the right - angle symbol for ∠5's related lines). So \(m\angle3 + m\angle6=90^{\circ}\) (because ∠3 and ∠6 are complementary angles, and complementary angles sum to \(90^{\circ}\)).

Step3: Compare \(m\angle5\) and \(m\angle3 + m\angle6\)

Since \(m\angle5 = 90^{\circ}\) and \(m\angle3 + m\angle6 = 90^{\circ}\), we can conclude that \(m\angle5=m\angle3 + m\angle6\).

Answer:

The statement \(m\angle5 = m\angle3 + m\angle6\) is true. \(m\angle5 = 90^{\circ}\) because it is a right angle, and \(m\angle3 + m\angle6=90^{\circ}\) because ∠3 and ∠6 are complementary angles.