ΔABC and ΔDEF are congruent respectively. If AB = 6 = DE, BC = 8 = EF and m∠B = 30°, then m∠D + m∠C = _________ .
Answer & explanation
Correct answer: option 4
According to the concept,
Since triangle ABC and triangle DEF are congruent and AB = 6+ DE, BC = 8 = EF and m\(\angle\)B = \({30}^\circ\) = m\(\angle\)E
Also, m\(\angle\)C = m\(\angle\)F ..(1.)
Hence, m\(\angle\)A = m\(\angle\)D ..(2.)
According to the concept,
m\(\angle\)C + m\(\angle\)A = \({180 - 30}^\circ\) ..(3.)
m\(\angle\)E + m\(\angle\)F = \({180 - 30}^\circ\) ..(4.)
From 1, 2, 3 and 4
m\(\angle\)D + m\(\angle\)C = \({180 - 30}^\circ\)
⇒ m\(\angle\)D + m\(\angle\)C = \({150}^\circ\)
Therefore, the value of m\(\angle\)D + m\(\angle\)C is \({150}^\circ\)