Question

in $\triangle abc$, $m\angle a = 43^\circ$ and $m\angle b = 85^\circ$. what is $m\angle c$?
$m\angle c = \square ^\circ$

Explanation:

Step1: Recall triangle angle sum theorem

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

Step2: Substitute known angles

We know \(m\angle A = 43^\circ\) and \(m\angle B = 85^\circ\), substitute these values into the formula: \(43^\circ + 85^\circ + m\angle C = 180^\circ\).

Step3: Calculate the sum of known angles

First, calculate \(43^\circ + 85^\circ = 128^\circ\).

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

Now, we have \(128^\circ + m\angle C = 180^\circ\). Subtract \(128^\circ\) from both sides: \(m\angle C = 180^\circ - 128^\circ = 52^\circ\).

Answer:

\(52\)