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Question

In the given circle with diameter AB, find the value of x.


Solution

angleABD = angleACD [angles in the same segment are equal] 

= 30º [angleACD = 30º given] 

AB is a diameter of the circle, angleADB = 90º [angle in a semi-circle is 90º] 

In Δ ABD, angleDAB + angleABD + angleADB = 180º

[sum of all the three angles of a triangle is 180º] 

Or, x + 30º + 90º = 180º Or, x = 180º – 90º – 30º = 60º.

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