Mathematics
In the given figure x°, y°, z° and p° are exterior angles of cyclic quadrilateral ABCD, then x° + y° + z° + p° is :
180°
270°
360°
720°
Answer
We know that,
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
In cyclic quadrilateral ABCD,
∠C = x°, ∠B = p°, ∠D = y° and ∠A = z°.
∴ x° + y° + z° + p° = ∠C + ∠D + ∠A + ∠B
We know that,
Sum of angles in a cyclic quadrilateral is 360°.
∴ ∠A + ∠B + ∠C + ∠D = 360°.
Hence, Option 3 is the correct option.
Related Questions
The figure shows a circle with centre O. AB is the side of regular pentagon and AC is the side of regular hexagon.
Find the angles of triangle ABC.
In the given figure, BD is a side of regular hexagon, DC is a side of a regular pentagon and AD is a diameter. Calculate :
(i) ∠ADC,
(ii) ∠BDA,
(iii) ∠ABC,
(iv) ∠AEC.
In the given figure, O is center of the circle and OABC is a rhombus, then :
x° + y° = 180°
x° = y° = 90°
x° + 2y° = 360°
x° = y° = 45°
Arcs AB and BC are of lengths in the ratio 11 : 4 and O is center of the circle. If angle BOC = 32°, the angle AOB is :
64°
88°
128°
132°
