In the given figure, AB || CD. If angle ABO = 45°
and angle COD = 100°, then find angle ODC.
Answers
Answer:
ODC=215,ABO=45,COD=100
Step-by-step explanation:
sum of all angles=360
ABO+COD+ODC=360
45+100+ODC=360
145+ODC=360
ODC=360-145
ODC=215
Given:
Angle ABO=45°
Angle COD=100°
To find:
The measure of angle ODC
Solution:
The measure of angle ODC is 35°.
We can find the angle by following the given steps-
We know that AB || CD and when two lines are parallel, the alternate interior angles formed are also equal.
We are given that the angle ABO=45°.
Since BC is the transversal, angle ABO is equal to the angle OCD.
So, angle ABO=angle OCD=45° (Alternate interior angles)
Now, in ΔCOD,
Angle COD=100°
The sum of all the angles in the ΔCOD is 180°.
Angle COD+Angle OCD+Angle ODC=180° (angle sum property)
On putting the values, we get
100°+45°+angle ODC=180°
145°+angle ODC=180°
Angle ODC=180°-145°
Angle ODC=35°
Therefore, the measure of angle ODC is 35°.