Question

∠rsl and ∠lst are a linear pair. find the value of x and each missing angle measure.
#14: x =
your answer
#14: m∠rsl =
your answer
#14: m∠lst =
your answer

Explanation:

Step1: Use linear - pair property

Since $\angle RSL$ and $\angle LST$ are a linear pair, their sum is $180^{\circ}$. So, $(5x + 17)+(2x-12)=180$.

Step2: Simplify the left - hand side

Combine like terms: $5x+2x + 17-12=180$, which gives $7x + 5=180$.

Step3: Solve for x

Subtract 5 from both sides: $7x=180 - 5=175$. Then divide both sides by 7: $x=\frac{175}{7}=25$.

Step4: Find $\angle RSL$

Substitute $x = 25$ into the expression for $\angle RSL$: $m\angle RSL=5x + 17=5\times25+17=125 + 17=142^{\circ}$.

Step5: Find $\angle LST$

Substitute $x = 25$ into the expression for $\angle LST$: $m\angle LST=2x-12=2\times25-12=50 - 12=38^{\circ}$.

Answer:

$x = 25$
$m\angle RSL=142^{\circ}$
$m\angle LST=38^{\circ}$