Question

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

Explanation:

Step1: Use angle - addition postulate

Since $\angle TUV=\angle TUW+\angle WUV$, we have $(17x - 16)=(5x + 3)+(10x - 5)$.

Step2: Simplify the right - hand side of the equation

$(5x + 3)+(10x - 5)=5x+10x+3 - 5=15x - 2$. 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 $m\angle TUW$

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

Step5: Find $m\angle WUV$

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

Step6: Find $m\angle TUV$

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

Answer:

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