The points A- B and C be on a circle in such a way that the - ABC-52- and - ACB-78- The measure of the angle subtended at the centre by the arc BC will be

The correct option is C 100^∘ In ΔABC , ∠ CAB=180^∘ (52^∘+78^∘)=50^∘ ∴ BOC=2×50^∘ =100^∘ ...

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Standard X

Mathematics

Arc/Chord Properties of Circles

The points ...

Question

The points $A, B a n d C$ be on a circle in such a way that the $∠ A B C = 52^{\circ}$ and $∠ A C B = 78^{\circ}$ . The measure of the angle subtended at the centre by the arc $B C$ will be

26^{\circ}

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50^{\circ}

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100^{\circ}

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115^{\circ}

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Solution

The correct option is C $100^{\circ}$
In $Δ A B C$ ,
$∠ C A B = 180^{\circ} - (52^{\circ} + 78^{\circ}) = 50^{\circ}$
$∴ B O C = 2 \times 50^{\circ}$
$= 100^{\circ}$

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The points A,BandC be on a circle in such a way that the ∠ABC=52∘ and ∠ACB=78∘. The measure of the angle subtended at the centre by the arc BC will be

The correct option is C 100∘In ΔABC,∠CAB=180∘−(52∘+78∘)=50∘∴BOC=2×50∘=100∘

The points $A, B a n d C$ be on a circle in such a way that the $∠ A B C = 52^{\circ}$ and $∠ A C B = 78^{\circ}$ . The measure of the angle subtended at the centre by the arc $B C$ will be

The correct option is C $100^{\circ}$
In $Δ A B C$ ,
$∠ C A B = 180^{\circ} - (52^{\circ} + 78^{\circ}) = 50^{\circ}$
$∴ B O C = 2 \times 50^{\circ}$
$= 100^{\circ}$