There are five professors teaching the introductory discrete mathematics class at someuniversity. the same final exam is given by all five professors. the exam score is aninteger between 0 and 100 (inclusive, that is, both 0 and 100 are possible). how manystudents must there be to guarantee that there are two students with the same professorwho earned the same final examination score?

If m∠abc = 70°, what is m∠abd? justify your reasoning.  using the addition property of equality, 40 + 70 = 110, so m∠abd = 110°.  using the subtraction property of equality, 70 − 30 = 40, so m∠abd = 30°.  using the angle addition postulate, 40 + m∠abd = 70. so, m∠abd = 30° using the subtraction property of equality.  using the angle addition postulate, 40 + 70 = m∠abd. so, m∠abd = 110° using the addition property of equality.