Question

the measure of angle 1 is (3x + 10)° and the measure of angle 4 is (4x − 15)°. what is the measure of angle 7? diagram of two parallel lines cut by a transversal, with angles labeled 1-8

Explanation:

Step1: Identify angle relationship

Angle 1 and angle 4 are alternate interior angles (since lines \(c\) and \(b\) are parallel, and line \(a\) is a transversal). So, \(m\angle1 = m\angle4\).
Set \(3x + 10 = 4x - 15\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(10 = x - 15\).
Add 15 to both sides: \(x = 25\).

Step3: Find \(m\angle1\)

Substitute \(x = 25\) into \(m\angle1 = 3x + 10\):
\(m\angle1 = 3(25) + 10 = 75 + 10 = 85^\circ\).

Step4: Relate angle 1 to angle 7

Angle 1 and angle 7 are corresponding angles (since \(c\parallel b\) and \(a\) is transversal), so \(m\angle7 = m\angle1 = 85^\circ\).

Answer:

\(85\)