Questions: NOTE: Angles not necessarily drawn to scale. x = □

NOTE: Angles not necessarily drawn to scale. x = □
Transcript text: NOTE: Angles not necessarily drawn to scale. \[ x=\square \]
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Solution

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Solution Steps

Step 1: Find the angle supplementary to 60°

Angles FAC and FAB are supplementary, meaning they add up to 180°. Since angle FAC is 60°, angle FAB is 180° - 60° = 120°.

Step 2: Find the sum of angles around point A

The sum of angles around a point is 360°. We have angles FAB (120°), BAC (80°), and CAD (x). Angle DAE is supplementary to angle EAF, however we do not have EAF given to us. We do not need to find EAF. The fourth angle, DAE, can be expressed as 360° - (120° + 80° + x).

Step 3: Calculate x

We know the angles around point A sum to 360°. Therefore, 120° + 80° + x = 180°. Simplifying, we get 200° + x = 180°. However, this is not correct. There are angles around a point, so it sums up to 360 degrees. So we have: 120° + 80° + x + DAE=360°. Since line EC is a straight line, it measures 180 degrees. So, 60+80+x =180. So, x=180-140=40.

Final Answer

40

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