Question

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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 =

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the triangle have angles \(A = 50^{\circ}\), \(B=70^{\circ}\), and \(C = \angle3\).
By the formula \(A + B+C=180^{\circ}\), we substitute \(A = 50^{\circ}\) and \(B = 70^{\circ}\) into the equation: \(50^{\circ}+70^{\circ}+m\angle3=180^{\circ}\).

Step2: Solve for \(m\angle3\)

Simplify the left - hand side of the equation: \(120^{\circ}+m\angle3=180^{\circ}\).
Subtract \(120^{\circ}\) from both sides of the equation: \(m\angle3=180^{\circ}- 120^{\circ}\).

Answer:

\(m\angle3 = 60^{\circ}\)