Question

Find the range of possible values of n.

Answer 1

B. 6 < n < 25

Explanation:

We are given the triangles WXY and WZY with sides XY and ZY congruent and equal to 8.

As the sides WX = 11 > WZ = 9.

Then, the angles opposite to WX will be greater than the angle opposite to WZ.

i.e. ∠WYX > ∠WYZ

i.e. (7n+5)° > 47°

i.e. 7n° > 42°

i.e. n >
`(42)/(7)`°

i.e. n > 6°

Since in ΔWXY, the sum of all three angles is 180°.

This means that (7n+5)° < 180°

i.e. 7n < 175°

i.e. n <
`(175)/(7)`°

i.e. n < 25°

Hence, we get that the range of n is 6 < n < 25.