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  • Write True or False and justify your answer in each of the following In Fig. 10.10, if AOB is a diameter and ∠ADC = 120°, then ∠CAB = 30°.

Write True or False and justify your answer in each of the following: In Fig. 10.10, if AOB is a diameter and \angleADC = 120°, then \angleCAB = 30°.

 

Answers (1)

True

Solution:

Given, AOB is a diameter and \angleADC = 120°

Join CA & CB

Since ADCB is a cyclic quadrilateral

\angleADC + \angleCBA = 180°  (Sum of opposite angles of a cyclic quadrilateral is 180°)

120° + \angleCBA = 180°

\angleCBA = 60°

In \triangleACB,

\angleCAB + \angleCBA +\angleACB = 180°  (angle sum property of a triangle)

\angleACB = 90° (Since, \angleACB is an angle in a semi-circle)

\angleCAB + 60° + 90° = 180°                 

\Rightarrow\angleCAB = 180° – 150° = 30°

Therefore the given statement is true.

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