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B is in the interior of angle AOC. C is in the interior of angle BOD. D is in the interior of angle COE. The measure of angle AOE is 162 degrees, COE is 68 degrees, and the measures of angles AOB, COD, and DOE are all equal. The question is to find the measure of angle DOA.

(it'd be a lot better if i'd post my sketch here, but anyway...)
I'm having a hard time what those three angles equal. If I knew what they equaled, I probably wouldn't have a hard time with the real question itself. I thought that angle AOC equaled 94 degrees just by measuring the angle with my protractor, but I think it's wrong because it may depend on how I draw the angles. My past results were that DOA equaled 123 degrees and 166. Can someone at least guide me to how you can find out what the measures of the three equal angles equal? Thanks much!

  • Math-Geometry -

    draw your figure.

    if <cod=<doe, then each must be 1/2 of 68, or 34 deg. But <aob= the same measure, or 34 deg. So now, figure out what boc is.
    <aob+<boc + <cod +<doe=162
    then <boc= 162-3*34

    check my thinking.
    This problem has nothing to do with a protractor, the angles are in the mind.

  • Math-Geometry -

    Angle BOC equals 60 degrees, so again, AOC is 94 degrees. If I add AOB, BOC, and COD, I get the measure of DOA, which is 128. Thank you!!!

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