in the adjoining figure,
Given : AB || CD , if
angle BAO= 58° and
angle OCD= 42° then
find the value of x°
Answers
Answer:
260°
Step-by-step explanation:
draw a line l parallel to AB,
And see my attachment.
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Answer:
Warning: please cross check my answer , because I'm not sure about it.
My answer is X°=260°
Step-by-step explanation:
Given:
AB||CD
angle BAO=58°
angle OCD=42°
To find:
X°
Construction:
Draw a transversal AC,
intersecting line AB and line CD at
point A and point C respectively.
Proof:
lineAB||lineCD ....... ( Given)
angle BAC + angle DCA =180° ........
( Interior Angle theorem.
lineAB || lineCD ,
On transvesal AC.)
therefore,
angle BAO+ angle OAC+
angle DCO+ angleOCA= 180° .........
( angle addition property)
therefore,
58°+angle p + 42° + angle q =180° .......
(1) ( construction)
therefore,
58°+42° + angle ( p+q)=180°
therefore,
100°+ angle( p + q)= 180°
therefore,
angle( p+q)= 180°-100°
therefore,
angle ( p+q)=80° ........ (2)
In ∆AOC,
angle OAC+ angle OCA+
angle AOC= 180° ..........
( Sum of measure of all angles of a
triangle is180°)
therefore,
angle( p+q) + angle AOC=180° .......
( from(1))
therefore,
80° + angle AOC= 180° .......
( from(2))
therefore,
angle AOC= 180°-80°
therefore,
angle AOC= 100° ..... (3)
As shown in the figure X° is a reflex angle, i.e. greater than 180° .
therefore , angle X and angle AOC are central angles of a common circle.
therefore,
X° + angle AOC = 360° ...........
( sum of measure of all the central angle of a circle is 360°)
therefore,
X° + 100° = 360° .......
( from(3))
therefore,
X° = 360°+100°
therefore,
X° = 260°
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