Answer:
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°
