asked 230k views
1 vote
MBEA =
148⁰
212°
74°
180°
B
C 74 A
E
D

MBEA = 148⁰ 212° 74° 180° B C 74 A E D-example-1

1 Answer

6 votes

Answer:

(b) 212°

Explanation:

You want the measure of major arc BEA intercepted by tangent AD and chord AB.

Angle

"Inscribed" angle DAB is the supplement of the one given, so is ...

∠DAB = 180° -74° = 106°

Arc

The measure of the arc that angle intercepts is double the measure of the angle:

arc BEA = 2×∠DAB = 2×106°

arc BEA = 212°

__

Additional comment

An inscribed angle is half the measure of the arc it intercepts. If you consider a point D' on arc EA, angle BAD' will have half the measure of arc AED'. This is true for D' located anywhere on arc EA, including at point A.

In the limit, as point D' approaches A, chord AD' approaches tangent AD. It should be no surprise, then, that angle DAB is half the measure of arc AEB.

<95141404393>

answered
User Lowitty
by
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