MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Angles in Same Segment of a Circle

In the figure...

Question

In the figure, $∠ D B C = 58^{\circ} .$ BD is a diameter of the circle. Calculate :

(i) $∠ B D C$

(ii) $∠ B E C$

(iii) $∠ B A C$

Open in App

Solution

Given $BD$ is diameter

$\angle DBC = 58^o$

(i) $\angle DCB = 90^o$ (angle in semi circle)

In $\triangle BDC$

$58+\angle BDC+90=180^o$

$\angle BDC = 32^o$

(ii) $ABEC$ is a cyclic quadrilateral

$\angle BDC = \angle BAC = 32^o$ (angle in the same segment)

Therefore $\angle BEC + 32 = 180^o$

$\angle BEC = 148^o$

(iii) $\angle BAC = 32^o$ (angle in the same segment)

Suggest Corrections

thumbs-up

8

Similar questions

Q. In the figure,

∠ D B C = 58^{\circ} . B D

is a diameter of the circle. Calculate

∠ B E C

Q. In the given figure, BD =DC and

∠

30^{0}

. Find the measure of

∠

BAC if O is centre of the circle.

Q. In the given figure, O is the centre of the circle. If BD = DC and

∠ D B C = 30^{\circ}

, find the measures of

∠ B A C

∠ B O C

Q. In the figure BD = DC and

∠ D B C = 25^{\circ}

. What is the value of

∠ B A C

Q. In the given figure,

B D = D C

∠ D B C = 30^{\circ}

what is the value of

∠ B A C

?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Circles and Quadrilaterals - Theorem 9

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Angles in Same Segment of a Circle

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon