Question
Download Solution PDFIn a circle, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced to F. If ∠ABC = 85º and ∠FAE = 24º, find the value of ∠BCD.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
∠ABC = 85º
∠FAE = 24º
AE is parallel to CD
AB is produced to F
Formula Used:
In a cyclic quadrilateral, opposite angles sum up to 180º.
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
Calculation:
We know in a cyclic quadrilateral opposite angles sum up to 180º. So,
∠ABC + ∠ADC = 180∘
∠ADC = 180∘ - 85∘ = 95∘
∠EAD = ∠ADC = 95∘ [Alternate interior angles of parallel lines CD and AE]
∠FAD = ∠FAE + ∠EAD
∠FAD = 24∘ + 95∘ = 119∘
∠BCD = ∠FAD = 119∘ [Exterior angle of a cyclic quadrilateral]
∴ The correct answer is 119∘
Last updated on May 28, 2025
-> The SSC has released the SSC CHSL exam calendar for various exams including CHSL 2025 Recruitment. As per the calendar, SSC CHSL Application process will be active from 23rd June 2025 to 18th July 2025.
-> The Exam Date for the SSC CHSL 2025 will be from 8th September 2025 to 18th September, 2025.
-> The SSC CHSL is conducted to recruit candidates for various posts such as Postal Assistant, Lower Divisional Clerks, Court Clerk, Sorting Assistants, Data Entry Operators, etc. under the Central Government.
-> The SSC CHSL Selection Process consists of a Computer Based Exam (Tier I & Tier II).
-> To enhance your preparation for the exam, practice important questions from SSC CHSL Previous Year Papers. Also, attempt SSC CHSL Mock Test.