Answer:
m∠R = 126° and UT = 104
Step-by-step explanation:
In the given triangles, two angles and one side is congruent so using ASA postulate both triangles are congruent.
IT can be written as:
ΔQRS = ΔTUV
When two triangles are congruent their respective sides and angles are congruent
So,
m∠R ≅ m∠U
And
UT = RQ
Using these
m∠R ≅ m∠U
[tex]10y-14 = 5y+56\\10y-5y-14 = 56\\5y = 56+14\\5y = 70\\\frac{5y}{5} = \frac{70}{5}\\y = 14[/tex]
Putting y = 14 in 10y-14
[tex]10(14)-14\\= 140-14\\= 126[/tex]
Hence,
m∠R = 126°
And
RQ = UT
[tex]14x-36 = 2x+84\\14x-2x-36 = 84\\12x = 84+36\\12x = 120\\\frac{12x}{12} = \frac{120}{12}\\x = 10[/tex]
Putting x = 10 in 2x+84
[tex]2(10)+84\\=20+84\\=104[/tex]
Hence,
m∠R = 126° and UT = 104
