Here is a triangle (ABC),A^ =80 and O is a point in triangle (not clear) ,?

CBO^=10 and OCB^= 30 ,AB=AC, AOB^=?Here is a triangle (ABC),A^ =80 and O is a point in triangle (not clear) ,?
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NOTE


I copied the problem incorrectly.


I have AB = BC


instead of AB = AC.


I'm tired.


Off hand, I don't see a way to do this if AB = AC.


Good luck.





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Given:


m鈭燗 = 80掳


Point O is in the interior of 螖ABC


m鈭燙BO = 10掳


m鈭燨CB = 30掳


AB = BC





Find:


m鈭燗OB





鈻柆鈻柆鈻柆鈻柆鈻柆鈻柆鈻柆鈻柆鈻柆鈻柆


1. m鈭燘OC + m鈭燨BC + m鈭燨CB = 180掳 so that m鈭燘OC = 140掳





2. 螖ABC is isosceles by definition, since AB = BC





3. m鈭燘CA = m鈭燘AC = 80掳, since base angles of isosceles 螖's are congruent





4. m鈭燘AC + m鈭燘CA + m鈭燗BC = 180掳





5. m鈭燗BC = 180掳 鈭?m鈭燘AC 鈭?m鈭燘CA = 20掳





6. m鈭燗BC = m鈭燗BO + m鈭燨BC


鈥堚€堚€堚€堚€堚€堚€堚€堚€堚€?鈥堚€堚€堚€?鈥堚€?20掳 = m鈭燗BO + 10掳


鈥堚€堚€堚€堚€堚€?m鈭燗BO = 10掳





7. OB = OB





8. 螖BOA 鈮?螖BOC by SAS





9. 鈭燗OB 鈮?鈭燙OB by corresponding parts of congruent 螖's





10. Therefore m鈭燗OB = 140掳








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