Answer:
x=45
Step-by-step explanation:
∠FEDstart color #1fab54, angle, F, E, D, end color #1fab54 and \blueD{\angle{x}}∠xstart color #11accd, angle, x, end color #11accd combine to form \angle{AED}∠AEDangle, A, E, D, which is a vertical angle with \goldD{\angle CEB}∠CEBstart color #e07d10, angle, C, E, B, end color #e07d10 because is opposite from \goldD{\angle CEB}∠CEBstart color #e07d10, angle, C, E, B, end color #e07d10.
Vertical angles are congruent, so \greenD{\angle{FED}} +\blueD{\angle{x}} = \goldD{\angle CEB}∠FED+∠x=∠CEBstart color #1fab54, angle, F, E, D, end color #1fab54, plus, start color #11accd, angle, x, end color #11accd, equals, start color #e07d10, angle, C, E, B, end color #e07d10.
Hint #22 / 2
\begin{aligned}\greenD{\angle{FED}} +\blueD x&= \goldD{160^\circ} \\\\ \greenD{115^\circ} + \blueD x &= \goldD{160^\circ} \\\\ \blueD x & = 45^\circ \end{aligned}
∠FED+x
115
∘
+x
x
=160
∘
=160
∘
=45
∘
