In the figure- angle ABC -65- and angle ACB -58- the measure of angle BDC isA- 57-B- 45- 68-D- 90-

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The Chords Corresponding to Congruent Arcs Are Congruent

In the figure...

Question

In the figure, angle ABC = 65^o and angle ACB = 58^o, the measure of angle BDC is

57^o

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45^o

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68^o

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90^o

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Solution

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In the figure, O is the centre of the circle and $∠ B D C = 42^{o}$ . The measure of $∠ A C B$ is

∠ A B P = ∠ A C Q, ∠ B A C = 68^{\circ}

∠ A B C

\begin{matrix} Properties & Quadrilaterals In a parallelogram ABCD If ∠ D = 115^{\circ},then the measure of ∠ A = & 68^{\circ} PQRS is a square such that PR and SQ intersect at O then the measure of ∠ P O Q = & 58^{\circ} The diagonals of a rectangle ABCD meet at O. If ∠ B O C = 44^{\circ}, then the measure of ∠ O A D = & 90^{\circ} If ABCD is a rectangle with ∠ B A C = 32^{\circ}, then the measure of ∠ D B C is = & 65^{\circ} \end{matrix}

In the given figure, $∠$ BAD = $65^{o}$ , $∠$ ABD = $70^{o}$ and $∠$ BDC = $45^{o}$ , Find :

(i) $∠$ BCD

(ii) $∠$ ACB

Hence, show that AC is a diameter.

∠ A B C = 69^{\circ}

∠ A C B = 31^{\circ} .

∠ B D C .

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