Question

In kite WXYZ , m∠XWY=38° and m∠ZYW=15° .

What is m∠WXY ?

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°

Answer 1

AC = CB, hence ΔABC is isosceles

the base angles 34 and x - 5 are therefore equal

x - 5 = 34 ( add 5 to both sides )

x = 39

and 4y = 180 - ( 2 × 34 ) = 112

4y = 112 ⇒ y = 28

Answer 2

x=39° ,y=28°

Explanation:

In the given figure

Side AC = Side BC

Hence ΔABC is an isosceles triangle.

⇒∠CAB =∠CBA (∵ angles opposite to equal sides are equal)

⇒ (x - 5)° = 34°

⇒ x = 39

Also in Δ ABC

∠ABC + ∠ACB + ∠CAB = 180°

(∵ Sum of all the interior angles of a triangle)

⇒ 34° + 34° + 4 y = 180°

⇒ 4 y =180°-68°

⇒ y=112°÷ 4

⇒y= 28°

Hence, x = 39° , y = 28°