9514 1404 393
Answer:
a) 60°
b) 60°
c) 70°
d) 90°
e) 40°
Step-by-step explanation:
The applicable relations are ...
- the sum of arcs in a circle is 360°
- an inscribed angle is half the measure of the arc it intercepts.
- the exterior angle where secants meet is half the difference of the intercepted arcs
- the interior angle where chords meet is half the sum of the intercepted arcs
- the angle made by a tangent and a chord is a degenerate case of an inscribed angle, where the vertex is coincident with one end of the intercepted arc
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a) The sum of ratio units is 3+5+6+4 = 18, which corresponds to the sum of arcs around the circle: 360°. So, each ratio unit stands for 360°/18 = 20°. The arcs around the circle are ...
FA = 60°, FC = 100°, CB = 120°, BA = 80°
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b) ∠BAC intercepts are CB, so is half its measure.
∠BAC = 60°
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c) ∠AEC is the exterior angle where secants EA and EC intercept arcs FA and CBA. The difference of those arcs is (CBA -FA) = (200° -60°) = 140°.
∠AEC = 140°/2
∠AEC = 70°
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d) Chords FB and AC intercept arcs FC = 100° and BA = 80°. The average of these measures is ...
∠FDC = (100° +80°)/2
∠FDC = 90°
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e) ∠GAB is an "inscribed" angle that intercepts arc BA, so has half its measure.
∠GAB = 40°
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Comment on arc/angle naming
The arc asked for in part (a) has a name that the Brainly censor doesn't like. It seems OK with the reverse designation, so we have used FA here to refer to that arc.
