If two angles have a common vertex and their arms form opposite rays (Fig. 5.41). Then, how many angles are formed
Solution:
Given, the figure represents two lines AC and BD which intersect at O.
Two angles have a common vertex and their arms form opposite rays.
We have to find how many angles are formed.
From the figure,
∠AOD, ∠BOA, ∠COB, ∠DOC, ∠AOA.
Since the lines intersect at a point O, the angles are ∠AOB, ∠BOC, ∠COD and ∠DOA
The linear pair of angles are
∠BOD = ∠1 + ∠4
∠AOC = ∠3 + ∠4
∠DOB = ∠2 + ∠3
∠COA = ∠2 + ∠1
The vertically opposite angles are ∠1, ∠3, ∠2 and ∠4.
Also, ∠AOB + ∠BOC + ∠COD + ∠DOA = ∠AOA = 360 degrees.
Therefore, 13 angles are formed.
✦ Try This: One angle is equal to three times its supplement. The measure of the angle is
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 81 (a)
If two angles have a common vertex and their arms form opposite rays (Fig. 5.41). Then, how many angles are formed
Summary:
If two angles have a common vertex and their arms form opposite rays (Fig. 5.41). Then, 13 angles are formed.
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