Question

in the figure below, m∠dba = 128°. (a) write an equation to find x. make sure you use an \=\ sign in your answer. equation: (b) solve for x. x =

Explanation:

Step1: Identify angle - sum relationship

We know that \(m\angle DBA=m\angle DBC + m\angle CBA\). Given \(m\angle DBA = 128^{\circ}\), \(m\angle CBA=49^{\circ}\) and \(m\angle DBC=(5x)^{\circ}\), the equation is \(5x + 49=128\).

Step2: Solve the equation for \(x\)

Subtract 49 from both sides of the equation \(5x+49 = 128\). We get \(5x=128 - 49\), so \(5x = 79\). Then divide both sides by 5, \(x=\frac{79}{5}=15.8\).

Answer:

(a) Equation: \(5x + 49=128\)
(b) \(x = 15.8\)