Question

question 4
congruent triangles - practice
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in the diagram, $\triangle abc \cong \triangle fde$.
find the value of $x$
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Explanation:

Step1: Find angle A in △ABC

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

Step2: Use congruent triangles property

Since \(\triangle ABC\cong\triangle FDE\), corresponding angles are equal. So, \(\angle F=\angle A = 24^\circ\)

Step3: Solve for x

We know that \(\angle F=(2x - 14)^\circ\) and \(\angle F = 24^\circ\). So, we set up the equation:
\(2x-14 = 24\)
Add 14 to both sides:
\(2x=24 + 14\)
\(2x=38\)
Divide both sides by 2:
\(x=\frac{38}{2}=19\)

Answer:

\(x = 19\)