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Question
In the triangle ABc, side BC is produced to D, $$\angle ACD=100^{\circ}$$ if BC=AC,then $$\angle ABC$$ is :
A
$$50^{\circ}$$
B
$$40^{\circ}$$
C
can't be determined
D
$$80^{\circ}$$
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Solution
Verified by Toppr
Correct option is B. $$50^{\circ}$$
In $$\triangle ABC,BC=AC\implies \angle BAC=\angle ABC$$
Given $$\angle ACD=100^{\circ}$$
As we know that
Sum of two interior angles is equal to opposite exterior angle
$$\implies \angle BAC+\angle ABC=100^{\circ}$$
$$\implies 2\angle ABC=100^{\circ}$$
$$\implies \angle ABC=\dfrac{100^{\circ}}{2}=50^{\circ}$$
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