Question

in the diagram, $\triangle abc \cong \triangle fde$. find the value of $x$.

Explanation:

Step1: Find angle A in △ABC

The sum of angles in a triangle is \(180^\circ\). In \( \triangle ABC \), we know \( \angle B = 48^\circ \) and \( \angle C = 108^\circ \). So, \( \angle A=180^\circ - 48^\circ - 108^\circ = 24^\circ \).

Step2: Use congruent triangles property

Since \( \triangle ABC \cong \triangle FDE \), corresponding angles are equal. So, \( \angle F=\angle A = 24^\circ \) and \( \angle D=\angle B = 48^\circ \) (so \( y = 48 \)). Also, \( \angle F=(2x - y)^\circ \). Substitute \( y = 48 \) and \( \angle F = 24^\circ \) into \( 2x - y=24 \).

Step3: Solve for x

We have the equation \( 2x - 48 = 24 \). Add 48 to both sides: \( 2x=24 + 48=72 \). Then divide by 2: \( x=\frac{72}{2}=36 \).

Answer:

\( 36 \)