Advertisements
Advertisements
प्रश्न
In the given figure, AB = AC = CD and ∠ADC = 38°. Calculate :
- Angle ABC
- Angle BEC
उत्तर
i. AC = CD
∴ ∠CAD = ∠CDA = 38°
∴∠ACD = 180° – 238° = 104°
∴∠ACB = 180° – 104° = 76° ...(Straight line)
Also, AB = AC
∴ ∠ABC = ACB = 76°
ii. By angle sum property,
∠BAC = 180° – 2 × 76°
∠BAC = 28°
∴ ∠BEC = ∠BAC = 28° ...(Angles in the same chord)
APPEARS IN
संबंधित प्रश्न
In the figure given alongside, AB and CD are straight lines through the centre O of a circle. If ∠AOC = 80° and ∠CDE = 40°, find the number of degrees in:
- ∠DCE,
- ∠ABC.
Calculate the angles x, y and z if :
`x/3 = y/4 = z/5`
In the given figure, ABC is a triangle in which ∠BAC = 30°. Show that BC is equal to the radius of the circumcircle of the triangle ABC, whose centre is O.
The given figure shows a circle with centre O such that chord RS is parallel to chord QT, angle PRT = 20° and angle POQ = 100°. Calculate:
(iii) angle QRS
The given figure shows a circle with centre O such that chord RS is parallel to chord QT, angle PRT = 20° and angle POQ = 100°. Calculate:
(iv) angle STR
In the given figure, O is the center of the circle and the length of arc AB is twice the length of arc BC. If ∠AOB = 100°,
find: (i) ∠BOC (ii) ∠OAC
In the given figure, an equilateral triangle ABC is inscribed in a circle with center O.
Find: (i) ∠BOC
(ii) ∠OBC
In the given figure, AB is a side of a regular hexagon and AC is a side of a regular eight-sided polygon.
Find:
(i) ∠AOB
(ii) ∠AOC
(iii) ∠BOC
(iv) ∠OBC
In the given figure, a square is inscribed in a circle with center O. Find:
- ∠BOC
- ∠OCB
- ∠COD
- ∠BOD
Is BD a diameter of the circle?
In the given figure, the lengths of arcs AB and BC are in the ratio 3:2. If ∠AOB = 96°, find:
- ∠BOC
- ∠ABC
