Question

6 fill in the blank 4 points if $m\angle cdf=(3x + 14)^{circ}$, $m\angle fde=(5x - 2)^{circ}$, and $m\angle cde=(10x - 18)^{circ}$, find each measure.
$x =$ type your answer...
$m\angle cdf=$ type your answer...
$m\angle fde=$ type your answer...
$m\angle cde=$ type your answer...

Explanation:

Step1: Use angle - addition postulate

Since $\angle CDE=\angle CDF+\angle FDE$, we can set up the equation $(3x + 14)+(5x - 2)=10x-18$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $(3x+5x)+(14 - 2)=8x + 12$. So the equation becomes $8x+12 = 10x-18$.

Step3: Solve for $x$

Subtract $8x$ from both sides: $12=10x - 8x-18$, which simplifies to $12 = 2x-18$. Then add 18 to both sides: $12 + 18=2x$, so $30 = 2x$. Divide both sides by 2: $x = 15$.

Step4: Find $m\angle CDF$

Substitute $x = 15$ into the expression for $m\angle CDF$: $m\angle CDF=3x + 14=3\times15+14=45 + 14=59^{\circ}$.

Step5: Find $m\angle FDE$

Substitute $x = 15$ into the expression for $m\angle FDE$: $m\angle FDE=5x - 2=5\times15-2=75 - 2=73^{\circ}$.

Step6: Find $m\angle CDE$

Substitute $x = 15$ into the expression for $m\angle CDE$: $m\angle CDE=10x-18=10\times15-18=150 - 18=132^{\circ}$.

Answer:

$x = 15$
$m\angle CDF = 59$
$m\angle FDE = 73$
$m\angle CDE = 132$