Question

the measure of the exterior angle equals
the sum of the measures of the
non - adjacent interior angles.
what is ( mangle5 )?
( mangle5 = 110^circ )
does ( mangle5 ) equal the sum of the measures
of its non - adjacent interior angles? explain.
yes, because ( 50^circ+60^circ = 110^circ ).
no, because ( 70^circ + 50^circ
eq110^circ ).
no, because ( 70^circ+60^circ
eq110^circ ).

Explanation:

Step1: Identify non - adjacent angles

For ∠5, the non - adjacent interior angles to it in the triangle are the \(50^{\circ}\) and \(60^{\circ}\) angles.

Step2: Calculate the sum of non - adjacent angles

The sum of the non - adjacent interior angles is \(50^{\circ}+60^{\circ}\). Calculating this, we get \(50 + 60=110^{\circ}\), which is equal to \(m\angle5 = 110^{\circ}\). So we check the options:

• Option 1: "Yes, because \(50^{\circ}+60^{\circ}=110^{\circ}\)." This matches our calculation.
• Option 2: \(70^{\circ}+50^{\circ}=120^{\circ}

eq110^{\circ}\), so this is wrong.

• Option 3: \(70^{\circ}+60^{\circ}=130^{\circ}

eq110^{\circ}\), so this is wrong.

Answer:

Yes, because \(50^{\circ}+60^{\circ}=110^{\circ}\).