Question : If $ABC \cong PQR$ and $\angle ABC = (x + 60)°$, $\angle PQR = (85 – 4x)°$, and $\angle RPQ = (3x + 65)°,$ then the value of $\angle ABC$ in degree is:
Option 1: 15°
Option 2: 5°
Option 3: 45°
Option 4: 65°
Correct Answer: 65°
Solution :
$\angle ABC$ = ($x$ + 60)°, $\angle PQR = (85 - 4x)°$
If $\triangle$ABC ≅ $\triangle$PQR,
⇒ $\angle ABC =\angle PQR$
⇒ $(x + 60)° = (85 -4x)°$
⇒ $x+4x = 85 - 60$
⇒ $5x = 25$
⇒ $x = 5$
$\therefore$ $\angle ABC = 5+60 = 65°$
Hence, the correct answer is 65°.
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