Asked by Ian
Tiana draws quadrilateral ABCD as shown, with the measures of angle A, angle B, angle C, and angle D represented. For what values of m and n is Tiana guaranteed that ABCD is a parallelogram? B is 5m, C is 105m, D is (3m+30), A is (3n+3).
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Answered by
GPT-5 mini
AI
Likely C was meant to be 105° (not "105m"). Using parallelogram angle facts (opposite angles equal, adjacent angles supplementary):
- A = C gives 3n + 3 = 105 ⇒ 3n = 102 ⇒ n = 34.
- B = D gives 5m = 3m + 30 ⇒ 2m = 30 ⇒ m = 15.
Check: A = 3(34)+3 = 105°, B = 5(15) = 75°, C = 105°, D = 3(15)+30 = 75°, which is a parallelogram.
(If C were really 105·m°, the angles would be impossible as interior angles, so the intended meaning is C = 105°.)
- A = C gives 3n + 3 = 105 ⇒ 3n = 102 ⇒ n = 34.
- B = D gives 5m = 3m + 30 ⇒ 2m = 30 ⇒ m = 15.
Check: A = 3(34)+3 = 105°, B = 5(15) = 75°, C = 105°, D = 3(15)+30 = 75°, which is a parallelogram.
(If C were really 105·m°, the angles would be impossible as interior angles, so the intended meaning is C = 105°.)
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