Question

Can someone please help with #16

Answer 1

Answer:

∠ WZX = 50°

XW is not an altitude.

Step-by-step explanation:

16. See the attached figure.

XW is the angle bisector of ∠ YXZ, hence, ∠ WXY = ∠ WXZ

Now, given that ∠ YXZ = 8x + 34 and ∠ WXY = 10x - 13

Hence, ∠ YXZ = 2 ∠ WXY

⇒ 8x + 34 = 2(10x - 13)

⇒ 8x + 34 = 20x - 26

⇒ 12x = 60

⇒ x = 5.

Hence, ∠ XZY = ∠ WZX = 10x = 50° (Answer)

Now, ∠ WXZ = ∠ WXY = 10x - 13 = 37°

Hence, from Δ WXZ,

∠ WZX + ∠ WXZ + ∠ XWZ = 180°

⇒ 50° + 37° + ∠ XWZ = 180°

⇒ ∠ XWZ = 93° ≠ 90°

Hence, XW is not an altitude. (Answer)