Question

in the figure below, m∠sqp = 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 \(m\angle SQP=m\angle PQR + m\angle RQS\). Given \(m\angle SQP = 128^{\circ}\), \(m\angle PQR=60^{\circ}\) and \(m\angle RQS = 4x^{\circ}\). So the equation is \(60 + 4x=128\).

Step2: Solve the equation for \(x\)

Subtract 60 from both sides of the equation \(60 + 4x=128\). We get \(4x=128 - 60\), so \(4x = 68\). Then divide both sides by 4: \(x=\frac{68}{4}=17\).

Answer:

(a) Equation: \(60 + 4x=128\)
(b) \(x = 17\)