Advertisements
Advertisements
Question
In a cyclic quadrilaterals ABCD, ∠A = 4x, ∠C = 2x the value of x is
Options
30°
20°
15°
25°
Solution
30°
Explanation;
Hint:
∠A + ∠C = 180° ...(Sum of the opposite angle of cyclic quadrilateral is 180°)
4x + 2x = 180°
x = `(180^circ)/6`
= 30°
APPEARS IN
RELATED QUESTIONS
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.
Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.
Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are `90^@-1/2A, 90^@-1/2B" and "90^@-1/2C`
In the figure m(arc LN) = 110°,
m(arc PQ) = 50° then complete the following activity to find ∠LMN.
∠ LMN = `1/2` [m(arc LN) - _______]
∴ ∠ LMN = `1/2` [_________ - 50°]
∴ ∠ LMN = `1/2` × _________
∴ ∠ LMN = __________
In a cyclic quadrilateral ABCD, if ∠A − ∠C = 60°, prove that the smaller of two is 60°
In the given figure, ABCD is a cyclic quadrilateral. Find the value of x.
PQRS is a cyclic quadrilateral such that PR is a diameter of the circle. If ∠QPR = 67° and ∠SPR = 72°, then ∠QRS =
In the figure, ▢ABCD is a cyclic quadrilateral. If m(arc ABC) = 230°, then find ∠ABC, ∠CDA, ∠CBE.
In the following figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD + ∠BED.
The three angles of a quadrilateral are 100°, 60°, 70°. Find the fourth angle.