Question

Rita is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 24. Which equation can she use as statement 5?. . (2x + 28) : 95 = 28 : 35. . (2x + 28) : 28 = 60 : 95. . (2x + 28) : 60 = 28 : 95. . (2x + 28) : 95 = 28 : 35

Answer 1

It seems that the first and the last options are exactly same. "(2x + 28) : 95 = 28 : 35" is the equation among the choices given in the question that she can use as statement. The correct option among all the options given in the question can be either the first or the last option. I hope the answer has helped you.

Answer 2

→If lines are parallel then their slopes are equal.

Given that , Segment ST is parallel to segment R Q.

If x = 24, we will start from option (1),and look at which option gives ,x= 24

$1.\frac{2 x +28}{95}=\frac{28}{35} \\\\ \frac{2 x +28}{95}=\frac{4}{5} \\\\ 2 x + 28=76 \\\\ 2 x = 76 -28 \\\\ 2 x = 48 \\\\ x=24\\\\ 2.\frac{2 x +28}{28}=\frac{60}{95} \\\\ \frac{ x +14}{28}=\frac{12}{19} \\\\ 19 x + 266=336 \\\\ 19 x = 336 -266 \\\\ 19 x = 70 \\\\ x=\frac{70}{19}\\\\ \frac{2 x +28}{60}=\frac{28}{95} {\text{and}} \frac{2 x +28}{95}=\frac{28}{35} {\text{will not give}}, x=24$

Option (1) $\frac{2 x +28}{95}=\frac{28}{35}$ gives, x=24.