In Fig. 5.5, the points A, O and B are collinear. Ray OC ⊥ ray OD. Check whether ∠AOD and ∠BOC are complementary.
Solution:
Given, the points A, O and B are collinear.
Ray OC ⊥ ray OD
We have to determine if ∠AOD and ∠BOC are complementary.
From the figure,
∠DOC = 90°
∠AOD = A°
∠BOC = 3a°
O is a point that lies on the line AB.
So, ∠AOD + ∠DOC + ∠BOC = 180°
∠AOD + 90° + ∠BOC = 180°
∠AOD + ∠BOC = 180° - 90°
∠AOD + ∠BOC = 90°
When the sum of the measures of two angles is 90°, the angles are called complementary angles.
Therefore, ∠AOD and ∠BOC are complementary.
✦ Try This: Two angles making a linear pair are always supplementary. State whether the given statement is true or false
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Sample Problem 14 (i)
In Fig. 5.5, the points A, O and B are collinear. Ray OC ⊥ ray OD. Check whether ∠AOD and ∠BOC are complementary
Summary:
In Fig. 5.5, the points A, O and B are collinear. Ray OC ⊥ ray OD. ∠AOD and ∠BOC are complementary as they are equal to 90 degrees
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