Question

question
$\triangle dsj \cong \triangle rcw$. if $\text{m}\angle d = 114^\circ$ and $\text{m}\angle j = 42^\circ$, find $\text{m}\angle c$.

answer attempt 2 out of 2

$\text{m}\angle c$ can be determined. $\text{m}\angle c = \square^\circ$.

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle DSJ\cong\triangle RCW\), corresponding angles are equal. So \(\angle S\) in \(\triangle DSJ\) corresponds to \(\angle C\) in \(\triangle RCW\).

Step2: Apply the triangle - angle sum theorem

In \(\triangle DSJ\), by the triangle - angle sum theorem (\(m\angle D + m\angle S+m\angle J=180^{\circ}\)).
We know \(m\angle D = 114^{\circ}\) and \(m\angle J = 42^{\circ}\). Substitute these values into the formula:
\(m\angle S=180^{\circ}-(m\angle D + m\angle J)\)
\(m\angle S=180^{\circ}-(114^{\circ}+ 42^{\circ})\)
\(m\angle S=180^{\circ}-156^{\circ}\)
\(m\angle S = 24^{\circ}\)

Answer:

\(24\)