In Fig. 9.3, if ∠AOB = 125°, then ∠COD is equal to
a. 62.5°
b. 45°
c. 35°
d. 55°
Solution:
Given, ∠AOB = 125°
We have to find the measure of angle COD.
From the figure,
We observe that ABCD is a quadrilateral circumscribing the circle.
We know that, the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.
The opposite sides are AB and CD
We have, ∠AOB + ∠COD = 180°
125° + ∠COD = 180°
∠COD = 180° - 125°
∠COD = 55°
Therefore, the measure of angle COD is 55°
✦ Try This: If PQRS is a quadrilateral circumscribing a circle. The angle subtended by the side PQ at the centre of the circle is 150°, then the measure of angle ROS is
Given, PQRS is a quadrilateral circumscribing a circle.
∠POQ = 150°
We have to find the measure of angle ROS.
We know that, the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.
The opposite sides are PQ and RS
We have, ∠POQ + ∠ROS = 180°
150° + ∠ROS = 180°
∠ROS = 180° - 150°
∠ROS = 30°
Therefore, the measure of angle ROS is 30°
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.1 Problem 2
In Fig. 9.3, if ∠AOB = 125°, then ∠COD is equal to a. 62.5°, b. 45°, c. 35°, d. 55°
Summary:
Two angles are said to be supplementary angles if they add up to 180 degrees. In Fig. 9.3, if ∠AOB = 125°, then ∠COD is equal to 55°
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