Question

find the measure of ∠ost. m∠ost =

Explanation:

Step1: Set up equation

Since $\angle OST$ and $\angle QTS$ are vertical - angles, they are equal. So we set up the equation $10x + 43=15x + 12$.

Step2: Solve for x

Subtract $10x$ from both sides: $43 = 5x+12$. Then subtract 12 from both sides: $5x=43 - 12=31$. So, $x=\frac{31}{5}=6.2$.

Step3: Find measure of $\angle OST$

Substitute $x = 6.2$ into the expression for $\angle OST$ which is $10x + 43$. So, $m\angle OST=10\times6.2 + 43=62 + 43=105^{\circ}$.

Answer:

$105$