Given AXYZ = ARST.mZR=(6n+1). m _Y=108°, and m _Z=(91-4)', what is the value of n?

A

Step-by-step explanation:

Given that the triangles are congruent then corresponding angles are congruent, thus

∠ S = ∠ Y = 108°

∠ T = ∠ Z = 9n - 4

Given ∠ R = 6n + 1

The sum of the 3 angles in Δ RST = 180°

Sum the 3 angles and equate to 180, that is

6n + 1 + 108 + 9n - 4 = 180 , simplify

15n + 105 = 180 ( subtract 105 from both sides )

15n = 75 ( divide both sides by 15 )

n = 5 → A

Let Y be the number of compact cars and 20 - Y be the number of full-sized car. If the total cost of 20 cars is $372, 000. Then we have: (Cost of compact car * number of compact car)+ (cost of full-sized car * number of full-sized car). So we have (15, 000 * Y) + (23, 000 * (20 -Y)) = 372, 000. Multiplying the expression, we have; 15, 000Y + 460, 000 - 23000Y = 372, 000. 15000Y - 23000Y = 372, 000 - 460, 000. -8000Y = - 88, 000. Hence Y = 11. Hence 11 compact cars were bought.