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Help with question in photo please

Help with question in photo please-example-1

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Answer:

124°

Explanation:

You want the measure of the angle marked (4+10x) where chords cross. The chords intercept arcs marked (9x+20) and (10x).

Angle relation

The measure of the angle where chords cross is the average of the measures of the intercepted arcs.

((9x +20) +(10x))/2 = 4 +10x

19x +20 = 20x +8 . . . . . . . . . multiply by 2

12 = x . . . . . . . . . . . . . . subtract (19x+8)

The angle at E is ...

4 +10(12) = 124

The measure of angle DEC is 124°.

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Additional comment

Arc DC is 128°; arc BU is 120°.

User Keddad
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