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1.(True or False) In the image below is the measure of angle ADB = 180 - the measure...

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anya4one | Student, Undergraduate | Honors

Posted December 28, 2012 at 1:02 PM via web

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1.(True or False) In the image below is the measure of angle ADB = 180 - the measure of angle A - the measure of angle C?

 


http://media.cheggcdn.com/media/ee4/ee4f58f3-6876-45ea-9d83-161c01ad37ba/phpQqUFoF.png

I think it's false as the angle are congruent not equal. Please correct me if I'm wrong. If I don't have this explained to me I can't complete the unit I am studying.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted December 28, 2012 at 4:44 PM (Answer #1)

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= You need to notice that the measure of angle `hat(ADB)`  may be evaluated in triangle `Delta ADB`  such that:

`hat(ADB) = 180^o - (hat A+ hat(ABD))`

You need to notice that the angle `hat(BDC)`  may be evaluated in triangle `Delta BDC`  such that:

`hat(BDC) = 180^o - (hatC+ hat(CBD))`

Adding the angles `hat(ADB)`  and `hat(BDC)`  yields:

`hat(ADB) + hat(BDC) = 360^o - hat A - hat C - (hat(ABD) + hat(CBD))`

`hat(ADB) = 360^o - hat A - hat C - hat B - hat(BDC)`

Hence, evaluting the measure of angle `hat(ADB)` , based on the drawing provided by the problem, yields `hat(ADB) = 360^o - hat A - hat C - hat B - hat(BDC` ), hence, the given answer is false.

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