Question

$\triangle adb \cong \triangle cdb$, find $m \angle c$.
a
|
32°
d
b
c
$m \angle c = ?°$

Explanation:

Step1: Recall properties of congruent triangles

Since \(\triangle ADB \cong \triangle CDB\), corresponding angles are equal. Also, in \(\triangle ADB\), we know \(\angle ABD = 90^\circ\) (right angle) and \(\angle ADB = 32^\circ\).

Step2: Calculate \(\angle A\) in \(\triangle ADB\)

The sum of angles in a triangle is \(180^\circ\). So, \(\angle A=180^\circ - 90^\circ - 32^\circ = 58^\circ\).

Step3: Use congruence to find \(\angle C\)

Because \(\triangle ADB \cong \triangle CDB\), \(\angle C=\angle A = 58^\circ\).

Answer:

\(58\)