Answer/Step-by-step explanation:
1. Antonio is correct. In a quadrilateral, opposite angles are supplementary. Since, (2x + 7), and (5x – 2) are opposite angles, they are supplementary. It is logical to set those two expressions equal to 180 due to it being supplementary. On the other hand, Erin is incorrect as he claims that the expressions, (2x + 7), and (5x – 2) are equal. While this is not the case because, in this quadrilateral, the opposite angles merit the supplementary feature when added together, however, the value of each expression could be any two numbers that add up to 180. Since those two expressions do not need to be and are not always necessarily equivalent, Erin is incorrect.
2.The steps I would take include using Antonio’s first step in setting (2x + 7), plus (5x – 2), equal to 180. Since, (2x + 7), and (5x – 2) are opposite angles, they are supplementary. It is logical to set those two expressions equal to 180 due to it being supplementary. Next, you will add like terms, resulting in 7x + 5 = 180. You will subtract 5 from both sides of the equation which is justified by the Subtraction Property of Equality. 7x = 175. Next, you will divide by 7, isolating the x. You get that x is equal to 25. You will then plug in the value of x into the expression for angle a. (5(25)-2) = 123 degrees