Question

lines r and s are parallel. find the value of x, then find the measure of ∠1 and ∠2. m∠1 = (70 - 2x)°, m∠2 = (81 - 3x)°. x = \square (type an integer or a fraction.) m∠1 = \square ° (type an integer or a fraction.) m∠2 = \square ° (type an integer or a fraction.)

Explanation:

Step1: Identify angle relationship

Since lines R and S are parallel, ∠1 and ∠2 are corresponding angles (or alternate interior, depending on diagram), so they are equal. Thus, \(70 - 2x = 81 - 3x\).

Step2: Solve for x

Add \(3x\) to both sides: \(70 + x = 81\).
Subtract 70: \(x = 81 - 70 = 11\).

Step3: Find \(m\angle1\)

Substitute \(x = 11\) into \(70 - 2x\): \(70 - 2(11) = 70 - 22 = 48\).

Step4: Find \(m\angle2\)

Since ∠1 = ∠2, \(m\angle2 = 48\) (or substitute into \(81 - 3x\): \(81 - 3(11) = 81 - 33 = 48\)).

Answer:

\(x = 11\)
\(m\angle1 = 48^\circ\)
\(m\angle2 = 48^\circ\)