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Question
In the given circle with diameter AB, find the value of x.
In the given circle with diameter AB, find the value of x.
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Solution
ABD = 
ACD [angles in the same segment are equal]
= 30º [
ACD = 30º given]
AB is a diameter of the circle, 
ADB = 90º [angle in a semi-circle is 90º]
In Δ ABD, 
DAB + 
ABD + 
ADB = 180º
[sum of all the three angles of a triangle is 180º]
Or, x + 30º + 90º = 180º Or, x = 180º – 90º – 30º = 60º.
ABD = ACD [angles in the same segment are equal]
= 30º [ACD = 30º given]
AB is a diameter of the circle, ADB = 90º [angle in a semi-circle is 90º]
In Δ ABD, DAB + ABD + ADB = 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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