Question

m∠opq = m∠por because they are alternate interior angles. m∠pqo = m∠qos because they are alternate interior angles. m∠por + x°+ m∠qos = 180° because the three angles form a straight line. so the value of x must be 50 now move all three vertices of the triangle above with your mouse.

Explanation:

Step1: Identify angle - equal relationships

Since $\angle{OPQ}$ and $\angle{POR}$ are alternate - interior angles, $m\angle{OPQ}=m\angle{POR} = 45^{\circ}$. Since $\angle{PQO}$ and $\angle{QOS}$ are alternate - interior angles, $m\angle{PQO}=m\angle{QOS}=85^{\circ}$.

Step2: Use the straight - line angle sum property

We know that $\angle{POR}+x^{\circ}+\angle{QOS}=180^{\circ}$ because they form a straight line. Substitute the known values of $\angle{POR}$ and $\angle{QOS}$ into the equation: $45 + x+85 = 180$.

Step3: Solve the equation for $x$

Combine like terms: $130 + x=180$. Then subtract 130 from both sides of the equation: $x=180 - 130$. So $x = 50$.

Answer:

$50$