Question

refer to the figure at the right if <2 = 7x +15 and <3 = 5x + 35, find x and the measure of <2 and <3.

Explanation:

Step1: Set up the equation

Since \(\angle2\) and \(\angle3\) are vertical angles, \(\angle2=\angle3\). So, \(7x + 15=5x+35\).

Step2: Solve for \(x\)

Subtract \(5x\) from both sides: \(7x-5x + 15=5x-5x+35\), which simplifies to \(2x+15 = 35\).
Subtract \(15\) from both sides: \(2x+15-15=35 - 15\), getting \(2x=20\).
Divide both sides by \(2\): \(x=\frac{20}{2}=10\).

Step3: Find the measure of \(\angle2\)

Substitute \(x = 10\) into \(\angle2=7x + 15\). So, \(\angle2=7\times10+15=70 + 15=85^{\circ}\).

Step4: Find the measure of \(\angle3\)

Substitute \(x = 10\) into \(\angle3=5x + 35\). So, \(\angle3=5\times10+35=50+35=85^{\circ}\).

Answer:

\(x = 10\), \(\angle2=85^{\circ}\), \(\angle3=85^{\circ}\)