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In the figure, YX−→− is a tangent to circle O at point X. mXB=52∘ mXA=104∘ What is the measure of ∠XYA ?

1 Answer

Shwetank Mauria

Mar 11, 2017

$m ∠ X Y A = 26^{\circ}$ $m/_XYA=26^@$

Explanation:

Let us join $O X$ $OX$ , $O A$ $OA$ , $O B$ $OB$ and $X A$ $XA$ .
enter image source here

As measure of arc $X A = 104^{\circ}$ $XA=104^@$ , $∠ X O A = 104^{\circ}$ $/_XOA=104^@$ and

$m ∠ X B A = \frac{1}{2} \times 104 = 52^{\circ}$ $m/_XBA=1/2xx104=52^@$

Further, as measure of arc $X B = 52^{\circ}$ $XB=52^@$ , $m ∠ X O B = 52^{\circ}$ $m/_XOB=52^@$ and

and $m ∠ B X Y = \frac{1}{2} \times 52^{\circ} = 26^{\circ}$ $m/_BXY=1/2xx52^@=26^@$

Hence, $m ∠ X Y A = m ∠ X Y B = m ∠ X B A - m ∠ B X Y = 52^{\circ} - 26^{\circ} = 26^{\circ}$ $m/_XYA=m/_XYB=m/_XBA-m/_BXY=52^@-26^@=26^@$

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