Question

think about the process in \\( \triangle a b c, m \angle b \\) is 4 times \\( m \angle a \\) and \\( m \angle c \\) is \\( 2^{\circ} \\) less than 5 times \\( m \angle a \\). what equation is used to solve for the variable \\( x \\)? find the measure of each angle. the figure is not drawn to scale. which of the following is the correct equation used to solve for the measure of each angle? \\( \bigcirc \\) a. \\( m \angle a - m \angle b + m \angle c = 180^{\circ} \\) \\( \bigcirc \\) b. \\( m \angle a + m \angle b - m \angle c = 180^{\circ} \\) \\( \bigcirc \\) c. \\( m \angle a - m \angle b - m \angle c = 180^{\circ} \\) \\( \bigcirc \\) d. \\( m \angle a + m \angle b + m \angle c = 180^{\circ} \\)

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, for \(\triangle ABC\), we have \(m\angle A + m\angle B + m\angle C=180^{\circ}\).

Answer:

D. \(m\angle A + m\angle B + m\angle C = 180^{\circ}\)