S
14x – 36/(10y – 14)
º
2x +84
(5y+56)°
> v
find the length of ut and the measure of zr.
mark this and return

UT = 104

∠R = 126°

Step-by-step explanation:

Part 1: Finding UT

The symbols on the triangles indicate that the triangles have the same side lengths.

That means 2x + 84 = 14x - 36

We can find the length of UT by solving for x

2x+84=14x−36

Step 1: Subtract 14x from both sides.

2x + 84 − 14x = 14x − 36 − 14x

−12x + 84 = −36

Step 2: Subtract 84 from both sides.

−12x + 84 − 84 = −36 − 84

−12x = −120

Step 3: Divide both sides by -12.

-12x / -12 = -120 / -12

x = 10

Now we know x=10, we can substitute 10 for x to get UT

UT = 2x + 84

UT = 2(10) + 84

UT = 20 + 84

UT = 104

So the length of UT is 104

Part 2: Finding ∠R

Since we know angle R is equal to angle U, we know

10y - 14 = 5y + 56

We can solve for y to find R

Step 1: Subtract 5y from both sides.

10y − 14 − 5y = 5y + 56 − 5y

5y − 14 = 56

Step 2: Add 14 to both sides.

5y−14+14=56+14

5y=70

Step 3: Divide both sides by 5.

5y/5 = 70/5

y=14

Now that we know y=14, we can substitute that value to find ∠R

∠R = 10y - 14

∠R = 10(14) - 14

∠R = 140 - 14

∠R = 126°

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