Question

the measure of ∠dcg is 145°. what is ( m_{angle dce} )? the diagram shows point c with several rays: cd going left, cg going right, and between them, rays ce and cf with angles ∠ecf = 20° and ∠fcg = 25°. options: 90°, 100°, 180°, 190°

Explanation:

Step1: Identify the angles to subtract

We know that \( \angle DCG = 145^\circ \), and we need to find \( \angle DCE \). From the diagram, the angles between \( \angle DCE \) and \( \angle DCG \) are \( \angle ECF = 20^\circ \) and \( \angle FCG = 25^\circ \). So we need to subtract these two angles from \( \angle DCG \).

Step2: Calculate the sum of the angles to subtract

First, find the sum of \( \angle ECF \) and \( \angle FCG \): \( 20^\circ + 25^\circ = 45^\circ \)

Step3: Subtract the sum from \( \angle DCG \)

Now, subtract this sum from \( \angle DCG \) to find \( \angle DCE \): \( 145^\circ - 45^\circ = 100^\circ \)

Answer:

\( 100^\circ \) (corresponding to the option with \( 100^\circ \))