Question

nayla
(20x + 7)^circ
carrie
(5x + 50)^circ
(5x + 3)^circ
maria
solve for x: x =
which two friends have the shortest distance between
them?
a. maria and nayla
b. carrie and maria
c. carrie and nayla
d. all three live equal distances from each other.
answer (only type in the letter!):

Explanation:

Step1: Use triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). So, \((20x + 7)+(5x + 50)+(5x + 3)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(20x+5x + 5x+7 + 50+3=180\), which gives \(30x+60 = 180\).

Step3: Solve for \(x\)

Subtract \(60\) from both sides: \(30x=180 - 60=120\). Then divide by \(30\): \(x=\frac{120}{30}=4\).

Step4: Find the angles

Carrie's angle: \(5x + 50=5\times4+50=20 + 50 = 70^{\circ}\).
Maria's angle: \(5x + 3=5\times4+3=20+3 = 23^{\circ}\).
Nayla's angle: \(20x + 7=20\times4+7=80 + 7=87^{\circ}\).

Step5: Use the triangle side - angle relationship

In a triangle, the side opposite the smaller angle is shorter. Since Maria's angle (\(23^{\circ}\)) is the smallest, the side opposite to it (Carrie and Nayla) is the shortest.

Answer:

\(x = 4\)
C