Question

Given ARWS = ATUV, find the values of x and y.
S
20
IT
V
3y + 7
29°
T
25
15
(8x - 27)°
R
U
X=
and y =

Answer 1

Answer:

x=11 degrees,y=6

Step-by-step explanation:

Here, given ΔRWS ≅ ΔTUV

Two triangle are said to be congruent to each other it they have exactly the same three sides and exactly the same three angles.

So, here RW = UT, WS = UV and SR = VT

⇒ 25 = 3y + 7

or, 3y = 25 - 7 = 18

or, y = 18/3 = 6

⇒ y = 6

In ΔTUV

By Angle Sum Property:

∠ TUV + ∠ UVT + ∠ UTV = 180°

or, 90° + 29°+ ∠ UTV = 180°

⇒∠ UTV = 180° - 119 = 61°

Now, by congruence rule: ∠ WRS = ∠ UTV

⇒ (8x - 27)° = 61°

or, 8x = 27° + 61° = 88°

or, x = 88/8 = 11°

⇒ x = 11°