Question

Erin says the first step is to set Latex: 2x+7 2 x + 7 equal to Latex: 5x-2\textsf{.} Antonio says the first step is to set Latex: 2x+7 2 x + 7 plus Latex: 5x-2 5 x − 2 equal to Latex: 180\textsf{.} Choose either Erin's or Antonio's statement and explain why it is correct or incorrect. If the statement is correct, explain how you know it's correct. If the statement is incorrect, explain why it's wrong. If you were to solve this problem, which steps would you take? Include any theorems, definitions, or reasons that explain the steps. Make sure you include all steps needed to solve for Latex: m\angle A\textsf{.}

Answer 1

*see attachment for the diagram

Answer/Step-by-step explanation:

1. Antonio's statement is correct because the sum of measure of the minor intercepted arc DE and the angle formed by tangents CE and CD outside the circle equal 180°.

According to the theorem. Therefore, the statement $2x + 7 + 5x - 2 = 180$ is correct.

2. To find the measure of <A, which is a central angle of the circle, find the value of x. Then find the measure of the intercepted arc.

According to the central angle theorem, the measure of a central angle equal the intercepted minor arc.

Therefore, the measure of the intercepted minor arc DE = m<A.

Step 1: find the value of x using the equation gotten in question 1.

$2x + 7 + 5x - 2 = 180$

Combine like terms

$7x + 5 = 180$

$7x + 5 - 5 = 180 - 5$

$7x = 175$

$\frac{7x}{7} = \frac{175}{7}$

$x = 25$

Step 2: find the measure of the minor intercepted arc DE, by substituting x = 25 into 5x - 2.

measure of arc DE = 5x - 2

= 5(25) - 2 = 125 - 2

measure of arc DE = 123°

Step 3: find the measure of centra angle A.

m<A = intercepted arc DE (central angle theorem)

m<A = 123°