Mathematics
In the given figure, ABCD is a cyclic quadrilateral whose side CD has been produced to E. If BA = BC and ∠BAC = 40°, find ∠ADE.
Circles
3 Likes
Answer
Given,
Quadrilateral ABCD is a cyclic quadrilateral.
∠ACB = ∠CAB = 40° [Angles opposite to equal sides are equal]
By angle sum property of a triangle we get,
In ΔABC,
⇒ ∠CAB + ∠CBA + ∠ACB = 180°
⇒ 40° + ∠CBA + 40° = 180°
⇒ ∠CBA + 80° = 180°
∴ ∠CBA = 100°
∠CBA + ∠CDA = 180° [Sum of opposite angles in a cyclic quadrilateral = 180°]
⇒ 100° + ∠CDA = 180°
⇒ ∠CDA = 80°
∴ ∠CDA + ∠ADE = 180° [Linear pairs]
⇒ 80° + ∠ADE = 180°
⇒ ∠ADE = 100°.
Hence, the value of ∠ADE is 100°.
Answered By
1 Like
Related Questions
In the given figure, ABCD is a cyclic quadrilateral in which ∠CAD = 25°, ∠ADB = 35° and ∠ABD = 50°. Calculate:
(i) ∠CBD
(ii) ∠CAB
(iii) ∠ACB
In the figure, AB is parallel to DC, ∠BCE = 80° and ∠BAC = 25°. Find :
(i) ∠CAD
(ii) ∠CBD
(iii) ∠ADC
In the given figure, AB is a diameter of a circle with centre O and chord ED is parallel to AB and ∠EAB = 65°. Calculate : (i) ∠EBA (ii) ∠BED (iii) ∠BCD
In the given figure, O is the centre of a circle and ABE is a straight line. If ∠CBE = 55°, find :
(i) ∠ADC
(ii) ∠ABC
(iii) the value of x.
