Question

option #4
your first option is to build the roof that has the measure of the two combining top angles of 78°.
what is the value of x?
x =
m∠aeb + m∠deb = 78°

Explanation:

Step1: Set up the equation

Given \(m\angle AEB=x^{\circ}\) and \(m\angle DEB=(2x + 6)^{\circ}\), and \(m\angle AEB+m\angle DEB = 78^{\circ}\). So the equation is \(x+(2x + 6)=78\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+2x+6=(1 + 2)x+6=3x+6\). The equation becomes \(3x+6 = 78\).

Step3: Solve for \(x\)

Subtract 6 from both sides: \(3x+6-6=78 - 6\), which gives \(3x=72\). Then divide both sides by 3: \(x=\frac{72}{3}\).

Answer:

\(x = 24\)