Problem: In triangle ABC,CA=CB. On CB square BCDE is constructed away from the triangle. If x is the number of degrees in angle DAB, then
Answer Choices:
A. x depends upon triangle ABC
B. x is independent of the triangle
C. x may equal angle CAD
D. x can never equal angle CAB
E. x is greater than 45∘ but less than 90∘
Solution:
∠ACB=180∘−2A. Since CA=CD,
∠CAD=21[180∘−(∠ACB+90∘)]
=21[180∘−(180∘−2A+90∘)]
=A−45∘
=A−X.
\therefore X=45^
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