Question

the measure of ∠dcg is 145°. what is m∠dce? 90° 100° 180° 190°

Explanation:

Step1: Use the angle - sum relationship

We know that \(m\angle DCG=m\angle DCE + m\angle ECF+m\angle FCG\). Given \(m\angle DCG = 145^{\circ}\), \(m\angle ECF = 20^{\circ}\), and \(m\angle FCG=25^{\circ}\). Let \(m\angle DCE=x\). Then the equation is \(x + 20^{\circ}+25^{\circ}=145^{\circ}\).

Step2: Solve for \(x\)

Subtract \(20^{\circ}+25^{\circ}\) from both sides of the equation. \(x=145^{\circ}-(20^{\circ} + 25^{\circ})\). First, calculate \(20^{\circ}+25^{\circ}=45^{\circ}\). Then \(x = 145^{\circ}-45^{\circ}\).

Answer:

\(100^{\circ}\)