Question

your first option is to build the roof that has the measure of the two combining top angles of 105°. what is the value of x? x = m∠aeb + m∠deb = 105°

Explanation:

Step1: Analyze the angle relationship

We know that \(m\angle AEB + m\angle DEB=105^{\circ}\), and \(m\angle AEB = 37^{\circ}\), \(m\angle DEB=x^{\circ}\).

Step2: Set up the equation

According to the angle - sum relationship, we have the equation \(37 + x=105\).

Step3: Solve the equation

Subtract 37 from both sides of the equation: \(x = 105 - 37\).

Answer:

\(x = 68\)