Advertisements
Advertisements
Question
In a quadrilateral ABCD, CO and DO are the bisectors of `∠`C and ∠D respectively. Prove that
`∠`COD = `1/2` (`∠`A+ `∠`B).
Advertisements
Solution
In ΔDOC
`∠`1+ `∠`COD + `∠`2 =180° [Angle sum property of a triangle]
⇒ `∠`COD = 180 - `∠`1- `∠`2
⇒ `∠`COD =180 - `∠`1+ `∠`2
⇒ `∠`COD = 180- `[1/2∠c+1/2∠d]`
[ ∵ OC and OD are bisectors of `∠`C and `∠`D represents ]
⇒ `∠`COD = 180-`1/2` (`∠`C and `∠`D)] ............1
In quadrilateral ABCD
`∠`A + `∠`B + `∠`C + `∠`D = 360°
`∠`C + `∠`D = 360 - `∠`A + `∠`B ..............(2) [ Angle sum property of quadrilateral]
Substituting (ii) in (i)
⇒ `∠`COD = 180 -`1/2`(360 - `∠`A + `∠`B ))
⇒ `∠`COD = 180 -180 +`1/2`(`∠`A +`∠`B )
⇒ `∠`COD =`1/2`(`∠`A +`∠`B )
APPEARS IN
RELATED QUESTIONS
Find the angle measure x in the given Figure
Find x + y + z
Find x in the following figure:
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13 Find all the angles of the quadrilateral.
In a quadrilateral ABCD, bisectors of angles A and B intersect at O such that ∠AOB = 75°, then write the value of ∠C + ∠D.
In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°. The angles of the triangle formed by joining the mid-points of the sides of this triangle are
Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.
In the following figure, P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. Prove that AD = 2CD.
A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is ______.
Three angles of a quadrilateral are equal. Fourth angle is of measure 120°. What is the measure of equal angles?
