Question

m∠6 = (2x + 3)° and m∠8 = (7x + 5)°. find the value of x, m∠6, and m∠8.
x = m∠6 = m∠8 =

Explanation:

Step1: Vertical angles

Vertical angles are equal. So \(m\angle3 = m\angle6\). Since \(m\angle3=(2x + 3)^{\circ}\) and \(m\angle6=(7x+5)^{\circ}\), we can set up the equation \(2x+3=7x + 5\).

Step2: Solve the equation

Subtract \(2x\) from both sides: \(3=5x + 5\).
Subtract \(5\) from both sides: \(3-5=5x\), so \(- 2=5x\).
Divide both sides by \(5\): \(x=-\frac{2}{5}=-0.4\).

Step3: Find \(m\angle6\)

Substitute \(x = - 0.4\) into \(m\angle6=(7x + 5)^{\circ}\).
\(m\angle6=7\times(-0.4)+5=-2.8 + 5=2.2^{\circ}\).

Step4: Find \(m\angle8\)

\(m\angle6\) and \(m\angle8\) are vertical angles. So \(m\angle8=m\angle6 = 2.2^{\circ}\).

Answer:

\(x=-0.4\), \(m\angle6 = 2.2^{\circ}\), \(m\angle8=2.2^{\circ}\)