ΔABC and ΔDEF are congruent respectively. If AB = 6 = DE, BC = 8 = EF and m∠B = 30°, then m∠D + m∠C = _________ .

150°

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 \({150}^\circ\)