Question

abcd is a cyclic quadrilateral in a circle with centre o. od║bc,∠dab=68°.find ∠bcd, ∠bod, ∠obd, ∠dbc
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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The correct answer to the given question regarding the angles of given cyclic quadrilateral is as follows:

1. ∠BOD = 136°
2. ∠BCD = 112°
3. ∠OBD = 22°
4. ∠DBC = 22°

Step-by-step explanation:

As per the question,

Given:

1. ABCD is the cyclic quadrilateral with O as it's centre.
2. OD ║ BC
3. ∠ DAB = 68°

To find:

• ∠BCD
• ∠BOD
• ∠OBD
• ∠DBC

In the cyclic quadrilateral ABCD,

Since, the angle by an arc at the centre is twice the angle on the circumference of the circle.

$\frac{1}{2}$ ∠BOD = ∠BAD

∠BOD = 2 X 68°

∠BOD = 136°

∠BCD = $\frac{1}{2}$  x reflex ∠BOD

∠BCD = $\frac{1}{2}$ (360° - 136°)

∠BCD =224° X $\frac{1}{2}$

∠BCD = 112°

As per the angle sum property,

∠OBD + ∠ODB +∠BOD = 180°

2 X ∠OBD = 180° - ∠BOD

Here, ∠OBD = ∠ODB since OD = OB

∠OBD = 22°

Since, OD is parallel to BC

In the alternate angles, the transversal is perpendicular to the parallel lines.

So, ∠BOD + ∠OBC = 180°

∠OBC = 180° - 136° = 44°

Since ∠OBD +∠DBC = ∠OBC = 44°

∠DBC = 44° - 22° = 22°

∠DBC = 22°

Therefore the required angles are found to be:

• ∠BOD = 136°
• ∠BCD = 112°
• ∠OBD = 22°
• ∠DBC = 22°

To learn more about cyclic quadrilaterals from the given links.

https://brainly.in/question/747324

https://brainly.in/question/38169

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