Question

determining an unknown angle measure
the measure of angle 1 is (3x + 10)° and the measure of angle 4 is (4x - 15)°.
what is the measure of angle 7?

Explanation:

Step1: Use vertical - angle relationship

Since angle \(1\) and angle \(4\) are vertical angles, \(3x + 10=4x-15\).

Step2: Solve for \(x\)

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

Step3: Find the measure of angle \(1\)

Substitute \(x = 25\) into \(3x+10\): \(3\times25 + 10=75 + 10=85^{\circ}\).

Step4: Use corresponding - angle relationship

Angle \(1\) and angle \(5\) are corresponding angles (because lines \(c\) and \(b\) are parallel and \(a\) is a transversal), so \(\angle5=\angle1 = 85^{\circ}\).

Step5: Use supplementary - angle relationship for angle \(7\)

Since \(\angle5+\angle7 = 180^{\circ}\) (linear pair), then \(\angle7=180^{\circ}-\angle5\). Substitute \(\angle5 = 85^{\circ}\), so \(\angle7=180 - 85=95^{\circ}\).

Answer:

\(95\)