Question

find the measure of ∠ors.

m∠ors=

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Explanation:

Step1: Identify the relationship between angles

Since lines \( p \) and \( N O \) are parallel (indicated by the arrows), and \( L M \) is a transversal, the angles \( (4x + 30)^\circ \) and \( (4x + 110)^\circ \) are same - side interior angles. Same - side interior angles are supplementary, so their sum is \( 180^\circ \).

$$ (4x + 30)+(4x + 110)=180 $$

Step2: Solve for \( x \)

Combine like terms:

$$ 8x+140 = 180 $$

Subtract 140 from both sides:

$$ 8x=180 - 140=40 $$

Divide both sides by 8:

$$ x=\frac{40}{8} = 5 $$

Step3: Find the measure of \( \angle ORS \)

We know that \( \angle ORS=(4x + 30)^\circ \). Substitute \( x = 5 \) into the expression:

$$ 4(5)+30=20 + 30=50 $$

Answer:

\( 50 \)