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 the property of vertical angles

Vertical angles are equal. Angle 1 and angle 4 are vertical angles. So, \(3x + 10=4x - 15\).

Step2: Solve for \(x\)

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

Step3: Find the measure of angle 1

Substitute \(x = 25\) into \(3x+10\). \(3\times25 + 10=75 + 10=85\). So, \(\angle1 = 85^{\circ}\).

Step4: Use the property of corresponding angles

Angle 1 and angle 5 are corresponding angles (since \(e\parallel b\) and \(a\) is a transversal). So, \(\angle5=\angle1 = 85^{\circ}\).

Step5: Use the property of vertical angles for angle 7

Angle 7 and angle 5 are vertical angles. So, \(\angle7=\angle5\).

Answer:

\(85^{\circ}\)