Question

In the given triangle, if ZW = ZX, WY = WX, then ∠WZX is equal to
(A) 70°
(B) 140°
(C) 40°
(D) 100°

Answer 1

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Answer 2

Answer:

(C) 40°

Explanation:

1- getting angle WYX:

We are given that ∠WYZ is 110°

We know that ∠WYZ and ∠WYX form a straight angle whose measure is 180°

Therefore:

∠WYZ + ∠WYX = 180°

110° + ∠WYX = 180°

∠WYX = 180° - 110° = 70°

2- getting angles ZXW and ZWX:

We are given that WY=WX

This means that:

∠WYX = ∠ZXW

∠ZXW = 70°

Since WZ=ZX, therefore:

∠ZXW = ∠ZWX = 70°

3- getting angle Z:

In triangle WXZ, the sum of the interior angles is 180.

This means that:

70° + 70° + ∠Z = 180°

∠Z = 180° - 70° - 70° = 40°

Hope this helps :)