Question

triangles!
the sum of all the interior (inside) angles of a triangle is always equal to 180°
∠_ + ∠_ + ∠___ = 180°
every exterior angle is supplementary to its adjacent interior angle.
∠_ + ∠_ = 180°
∠_ + ∠_ = 180°
the measure of an exterior angle is equivalent to the sum of the remote interior angles.
exterior ∠ sum of interior ∠
∠_ = ∠_ + ∠___
∠_ = ∠_ + ∠___
remote interior angles do not share a vertex w/ the exterior angle

Explanation:

Step1: Sum of interior angles

The sum of interior angles of a triangle is \(180^{\circ}\). So, \(\angle1+\angle2+\angle3 = 180^{\circ}\)

Step2: Supplementary angles

Exterior angle and adjacent interior angle are supplementary. So, \(\angle1+\angle5=180^{\circ}\), \(\angle3+\angle4 = 180^{\circ}\)

Step3: Exterior angle theorem

Exterior angle is equal to sum of remote interior angles. So, \(\angle4=\angle1+\angle2\), \(\angle5=\angle2+\angle3\)

Answer:

\(\angle1+\angle2+\angle3 = 180^{\circ}\); \(\angle1+\angle5=180^{\circ}\), \(\angle3+\angle4 = 180^{\circ}\); \(\angle4=\angle1+\angle2\), \(\angle5=\angle2+\angle3\)