Question

determining angle measures
the measure of \\( \angle dcg \\) is \\( 145 ^ { \circ } \\).
what is \\( m \angle dce \\)?
\\( 90 ^ { \circ } \\)
\\( 100 ^ { \circ } \\)
\\( 180 ^ { \circ } \\)
\\( 190 ^ { \circ } \\)

Explanation:

Step1: Use angle - sum relationship

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

Step2: Solve the equation for \(x\)

Simplify the left - hand side of the equation: \(x+(20 + 25)=x + 45\). So, \(x+45=145\). Subtract 45 from both sides of the equation: \(x=145 - 45\).

Answer:

\(100^{\circ}\)