Question

in the figure shown, ∠4 is an exterior angle. what is another way ∠3 and ∠4 are related? angles 3 and 4 form a straight angle. that means m∠3 + m∠4 = 180°. what is m∠3? m∠3 = ?° (figure: a triangle with angles 50°, 70°, and ∠3, with ∠4 as an exterior angle to ∠3)

Explanation:

Step1: Recall Triangle Angle Sum

The sum of angles in a triangle is \(180^\circ\). The triangle has angles \(50^\circ\), \(70^\circ\), and \(\angle 3\).

Step2: Calculate \(m\angle 3\)

Using the triangle angle sum formula: \(m\angle 3 + 50^\circ + 70^\circ = 180^\circ\).
Simplify: \(m\angle 3 + 120^\circ = 180^\circ\).
Subtract \(120^\circ\) from both sides: \(m\angle 3 = 180^\circ - 120^\circ = 60^\circ\).

Answer:

\(60\)