Answer:
x = 5 and y = 7
Step-by-step explanation:
Given that,
PT = x+2, TR=y, QT=2x, TS=y+3
We need to find the value of x and y.
The diagonal of a parallelogram bisect each other. It means,
PT = TR and QT = TS
ATQ,
y = x+2 ...(1)
and
y+3 = 2x ....(2)
Subtracting equation (1) and (2).
y-(y+3) = x+2-2x
y-y-3 = 2-x
-3 = 2-x
x = 2+3
x = 5
Put the value of x in equation (1).
y = 5 + 2
y = 7
Hence, the values of x and y are x = 5 and y = 7.
The value of the angle ∠x will be ∠x = 128°. Then the correct option is C.
<h3>What is the triangle?</h3>A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangle is given below.
The sum of the two interior angle is equal to the third exterior angle.
m∠x = (198 − 5n)°
m∠y = (5n + 37)°
m∠z = (n + 7)°
We know that
∠x = ∠y + ∠z
198 - 5n = 5n + 37 + n + 7
11n = 154
n = 14
Then the value of the angle ∠x will be
∠x = 198 – 5 × 14
∠x = 128°
Then the correct option is C.
The complete question is given below.
More about the triangle link is given below.
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