Question

find the measure of ∠ost. (10x + 43)° (15x + 12)° m∠ost =

Explanation:

Step1: Set up equation based on vertical - angle property

Vertical angles are equal. $\angle OST$ and the angle with measure $(15x + 12)^{\circ}$ are vertical angles, and the angle with measure $(10x + 43)^{\circ}$ and the angle with measure $(15x + 12)^{\circ}$ are supplementary (linear - pair, sum to $180^{\circ}$). So, we set up the equation $10x+43 + 15x+12=180$.
$10x+15x+43 + 12=180$
$25x+55 = 180$

Step2: Solve for $x$

Subtract 55 from both sides of the equation:
$25x=180 - 55$
$25x=125$
Divide both sides by 25:
$x=\frac{125}{25}=5$

Step3: Find the measure of $\angle OST$

Since $\angle OST$ and the angle with measure $(15x + 12)^{\circ}$ are vertical angles, we substitute $x = 5$ into $15x+12$.
$15\times5+12=75 + 12=87$

Answer:

$87$