Question

LDBC=70° and LCAB=30° find LBCD​

Answer 1

Given:-

• ∠DBC = 70°
• ∠CAB = 30°

To find:-

• ∠BCD

Answer:-

We know that angles in the same segment are equal.

So, ∠DAC = ∠DBC

→ ∠DAC = 70°

Now, we know that, the opposite angles in a cyclic quadrilateral are supplementary, that is, their sum is 180°

So, ∠DAB + ∠BCD = 180°

→ ∠DAC + ∠CAB + ∠BCD = 180°

→ 70° + 30° + ∠BCD = 180°

→ 100° + ∠BCD = 180°

→ ∠BCD = 180° - 100°

→ ∠BCD = 80° Ans

Extra knowledge:-

• Two circles are congruent only if their radii are equal
• Equal chords of a circle subtend equal angles at the centre.
• If two arcs are congruent, the corresponding chords are equal.
• The perpendicular from the centre of the circle bisects the chord.
• Equal chords of a circle are equidistant from the centre.
• The angle subtended by an arc of a circle is double the angle subtended by it at any point on the remaining part of the circle.
• The angle in a semicircle is 90°.
• The opposite angles of a cyclic quadrilateral are supplementary.
• If one side of a cyclic quadrilateral is produced, then the exterior angle so formed is equal to the interior opposite angle.