In this problem, we're going to explain why any trapezoid that can be inscribed in a circle must be an isosceles trapezoid. in this figure, let's assume without loss of generality that segments ab and dc are parallel. by the end of this problem, we want to show that ∠d ≅ ∠c.

1. explain why ∠a must be supplementary to ∠d.

2. explain why ∠a must also be supplementary to ∠c.

3. now we know that ∠a is supplementary to ∠d and is also supplementary to ∠c. explain why that proves that ∠d must be congruent to ∠c.

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24