The exterior angle bisectors of angle B and angle C intersect on point O. angle BOC=70. Find angle OAC.

Mariyah Best

Mariyah Best

Open question

2022-08-22


The exterior angle bisectors of B and C intersect on point O. B O C = 70 ° .
Find O A C.

Answer & Explanation

matracavade

matracavade

Beginner2022-08-23Added 11 answers

We know that exterior angle of b = 2 β = A + 180 c Suppose exterior angle of c is 2 α, so
2 β = A + 180 2 α
but α + β = 180 70 = 110,so
A = 220 180 = 40
That's was part one, now part two. Let's prove that AO is bisector. Let's take the heights on BC , (AB) and (AC), where (AB) mean line AB. So as BO and CO are bisectors, then it's easy to prove that O - is center of some circle , which intersect BC, (AC), (AB) , so O is lying on AO - bisector, so O A C = 20

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