`angle ABD = 54^@ and angleBCD = 43^@`, calculate the `angleBDA`

angle ABD = 54^@ and angleBCD = 43^@ , calculate the angleBAD

angle ABD = 54^@ and angleBCD = 43^@ , calculate the angleACD

ABCD is a cyclic quadrilateral in which AC and BD are its diagonals.If angleDBC = 70^@ and angle BAC = 30^@ find angleBCD

In Fig. 6.43, if PQ bot PS , PQ || SR, angle SQR = 28^@ and angle QRT = 65^@ , then find the values of x and y.

A ray of light passes from air to glass (mu = 1.5) at an angle of 30^@ .Calculate angle of refraction.

A ray of light suffers minimum deviation,while passing through a prism of refractive index 1.5 and refracting angle 60^@ ,calculate the angle of deviation and angle fo incidence.

A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45^@ and the angle of depression of the base is 30^@ . Calculate the distance of the cliff from the ship and the height of the cliff.

A man on the deck of a ship is 12 m above water level. He observes that the angle of elevation of the top of a cliff is 45^@ , and the angle of depression of the base is 30^@ . Calculate the distance of the cliff from the ship and the height of the cliff.

ABCD is a quadrilateral in which AD = BC and angle DAB =angle CBA (see Fig. 7.17). Prove that (i) triangle ABD cong triangle BAC (ii) BD = AC (iii) angle ABD = angle BAC .

In Fig. 6.40, angle X = 62^@, angle XYZ = 54^@ . If YO and ZO are the bisectors of angle XYZ and angle XZY respectively of triangle XYZ , find angle OZY and angle YOZ .