The value of x, rounded to the nearest hundredth, is approximately 11.27.
The value of y, rounded to the nearest hundredth, is approximately 2.99.
How to find the values of x and y
To find the values of x and y in the given kite TCRL, use the properties of a kite, which states that the two pairs of adjacent angles formed by the intersecting diagonals are congruent.
In this case, we have the following angle measurements:
m∠CTR = (7x - 12)°
mTCR = (8x + 32)°
m∠LRT = (9y + 40)°
mTLR = (4y)°
According to the property of a kite, set up the following equations:
m∠CTR = m∠LRT
7x - 12 = 9y + 40
mTCR = mTLR
8x + 32 = 4y
Now, solve these equations to find the values of x and y.
From the equation 7x - 12 = 9y + 40, simplify and rearrange it:
7x - 9y = 52
From the equation 8x + 32 = 4y, simplify and rearrange it:
8x - 4y = -32
We now have a system of linear equations:
7x - 9y = 52
8x - 4y = -32
To solve this system, use any method such as substitution or elimination. Here, let's use the elimination method:
Multiply the first equation by 4, and the second equation by 9 to eliminate y:
28x - 36y = 208
72x - 36y = -288
Subtract the second equation from the first equation:
(28x - 36y) - (72x - 36y) = 208 - (-288)
-44x = 496
Divide both sides by -44:
x = -496 / -44
x ≈ 11.27
Therefore, the value of x, rounded to the nearest hundredth, is approximately 11.27.
To find the value of y, substitute the value of x back into one of the original equations.
Let's use the equation 7x - 9y = 52:
7(11.27) - 9y = 52
78.89 - 9y = 52
Subtract 78.89 from both sides:
-9y = 52 - 78.89
-9y = -26.89
Divide both sides by -9:
y ≈ -26.89 / -9
y ≈ 2.99
Therefore, the value of y, rounded to the nearest hundredth, is approximately 2.99.
Find complete question below
TCRL is a kite as shown where m∠CTR = (7x-12)°, mTCR = (8x +32)°, m∠LRT = (9y+40)°, and mTLR = (4y)°.
4. What is the value of x? Round your answer to the nearest hundredth.
5. What is the value of y? Round your answer to the nearest hundredth.