ΔABC and ΔDEF are congruent triangles respectively. If AB = 6 = DE, BC = 8 = EF and m ∠B = 30°, then m ∠D + m ∠C =_________.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 150°.
As the triangles are congruent and as per the given sides,
m∠ A = m∠ D
⇒ m∠ B = m∠ E and hence
⇒ m∠ C = m∠ F
Now, m∠ A + m∠ B + m∠ C = 180º
m∠ A + m∠ C + 30º = 180º
⇒ m∠ A + m∠ C = 150º.......(1)
Similarly, m∠ D + m∠ F = 150º......(2)
Now adding (1) and (2), m∠ A + m∠ C + m∠ D + m∠ F = 300º
Now as m∠ A = m∠ D and m∠ C = m∠ F
⇒ 2m∠ D + 2m∠ C = 300º
⇒ m∠ D + m∠ C = 150º