Question

find x........if o is 78.

Answer 1

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${\sf{⟹ \ \angle O \ = \ 78°}}$

${\sf{⟹ \ \angle AOC \ = \ 180 - 78}}$ (leniar pair)

${\sf{⟹ \ \angle AOC \ = \ 102°}}$

Now, in triangle AOC

${\sf{↣ \ AO \ = \ CO}}$ (Radius of circle)

hence,

${\sf{↣ \ \angle ACO \ = \ \angle CAO }}$

${\sf{↣ \ Let \ \angle ACO \ and \ \angle CAO \ be \ x}}$

Now,

${\sf{↣ \ x + x + 102 \: = \: 180}}$

${\sf{↣ \ 2x \: = \: 180 \: - \: 102}}$

${\sf {↣ \ 2x \: = \: 78}}$

${\sf{↣ \ x \: = \: \frac{78}{2} }}$

${\sf { ↣ \ x \: = \: 39}}$

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