Question

1. if m∠tuw=(5x + 3)°, m∠wuv=(10x - 5)°, and m∠tuv=(17x - 16)°, find each measure.

x =
m∠tuw =
m∠wuv =
m∠tuv =

Explanation:

Step1: Use angle - addition postulate

Since $\angle TUV=\angle TUW+\angle WUV$, we can set up the equation $(17x - 16)=(5x + 3)+(10x - 5)$.

Step2: Simplify the right - hand side of the equation

Combine like terms on the right - hand side: $(5x + 3)+(10x - 5)=5x+10x+3 - 5=15x - 2$. So the equation becomes $17x-16 = 15x - 2$.

Step3: Solve for $x$

Subtract $15x$ from both sides: $17x-15x-16=15x-15x - 2$, which simplifies to $2x-16=-2$. Then add 16 to both sides: $2x-16 + 16=-2 + 16$, so $2x=14$. Divide both sides by 2: $x = 7$.

Step4: Find $\angle TUW$

Substitute $x = 7$ into the expression for $\angle TUW$: $m\angle TUW=(5x + 3)^{\circ}=(5\times7 + 3)^{\circ}=(35 + 3)^{\circ}=38^{\circ}$.

Step5: Find $\angle WUV$

Substitute $x = 7$ into the expression for $\angle WUV$: $m\angle WUV=(10x - 5)^{\circ}=(10\times7 - 5)^{\circ}=(70 - 5)^{\circ}=65^{\circ}$.

Step6: Find $\angle TUV$

Substitute $x = 7$ into the expression for $\angle TUV$: $m\angle TUV=(17x - 16)^{\circ}=(17\times7 - 16)^{\circ}=(119 - 16)^{\circ}=103^{\circ}$.

Answer:

$x = 7$
$m\angle TUW=38^{\circ}$
$m\angle WUV=65^{\circ}$
$m\angle TUV=103^{\circ}$