Bissoy.com
Doctors Medicines MCQs Q&A

In the figure given below, ACDE is a cyclic quadrilateral and PAB || EC. If ∠BAC = 35° and ∠DCE = 25°, then what is the value of ∠DEC?

In the figure given below, ACDE is a cyclic quadrilateral and PAB || EC. If ∠BAC = 35° and ∠DCE = 25°, then what is the value of ∠DEC? Correct Answer 85°

GIVEN:

PAB || EC

∠BAC = 35° and ∠DCE = 25°

CONCEPT:

Alternate angles are always equal.

CALCULATION:

∠ACE = ∠BAC = 35°

∠AEC + ∠ACE + ∠EAC = 180°

⇒ 35° + 35°+ ∠EAC = 180°

⇒ ∠EAC = 110°

⇒ ∠EDC = 180° – 110° = 70°

In ∆EDC:

∠EDC + ∠ECD + ∠DEC = 180°

70° + 25°+ ∠DEC = 180°

∴ ∠DEC = 85°

Related Questions

i. ∠ACD = ∠ABC + ∠BAC ii. ∠ACE = ∠BAC iii. ∠DCE = ∠ABC নিচের কোনটি সঠিক?
Given: Stock of stationery on Jan. 1,2011 Rs. 400.Stock of stationery on Dec. 31,2011 Rs.100. Payment for stationery during 2011 Rs.1200. Creditor for stationery on Dec. 31, 2011 Rs. 150.  What is the amount of stationery that will be posted to the Income and Expenditure A/c for the year ending Dec.31,2011?
How many of the following statements are correct? i) All cyclic graphs are complete graphs. ii) All complete graphs are cyclic graphs. iii) All paths are bipartite. iv) All cyclic graphs are bipartite. v) There are cyclic graphs which are complete.
ABCD is a cyclic quadrilateral in which AB = BC, O is the centre of circle and one of diagonal of cyclic quadrilateral passes through the centre of circle and ∠DCA = 40°. Find the ∠BAD.
ABCD is a cyclic quadrilateral in which O is the center of the circle and one of the diagonal of the cyclic quadrilateral passes through the center of the circle and ∠DCA = 30°. Find the measure of ∠CAD.
ABCD is a cyclic quadrilateral in which AB = BC = 6 cm, O is the center of the circle and one of the diagonals of the cyclic quadrilateral passes through the center of the circle. Find the area of ΔABC.
ABCD is a cyclic quadrilateral in which AB = BC = 8 cm, O is the center of the circle and one of the diagonal of the cyclic quadrilateral passes through the center of the circle. Find the radius of the circle.
Consider the following a) Opposite angles of a cyclic quadrilateral are complementary b) The angle at the centre of a circle is twice the angle at the circumference. c) A cyclic quadrilateral has all its vertices on the circumference of the circle Which of the above statement is/are correct?
Which of the following propertie(s) of circle is/are correct? I. Opposite angles of a cyclic quadrilateral are supplementary. ABCD is cyclic quadrilateral as its vertices lie on the circle. II. The degree measure of an arc is equal to twice the measure of an angle inscribed in the opposite arc.
In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that ∠DBC is 50° and ∠BAC is 40°. Find the value of ∠BCD