Question

1. line n is represented by $y = \frac{3}{5}x - 3$. match each equation to the term that accurately describes its relationship to line m.

$y = -1\frac{2}{3}x + 3$
$y = -0.6x + 3$
$y = 0.6x + 3$
perpendicular
neither parallel nor perpendicular
parallel

1. in $\triangle abc$, $m\angle a = 56^\circ$ and $m\angle b = 73^\circ$. what is $m\angle c$?

$m\angle c = \underline{\quad\quad}$ $^\circ$

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle A + m\angle B + m\angle C = 180^\circ\).

Step2: Substitute known angles

We know \(m\angle A = 56^\circ\) and \(m\angle B = 73^\circ\). Substitute these values: \(56^\circ + 73^\circ + m\angle C = 180^\circ\).

Step3: Calculate sum of known angles

\(56 + 73 = 129\), so \(129^\circ + m\angle C = 180^\circ\).

Step4: Solve for \(m\angle C\)

Subtract \(129^\circ\) from both sides: \(m\angle C = 180^\circ - 129^\circ = 51^\circ\).

Answer:

\(51\)