Question

Find the unknown angle x in the figure if AD=DC, AE=BC and (ACB) = 750 ? a) 350 b) 40° c) 45° d) 50°

Answer 1

Given: AD=BD=AC ∠CAE=75

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In △ABD

AD=BD

∠ABD=∠BAD=x (Isosceles triangle property)

∠ADC=∠ABD+∠BAD=2x (Exterior angle property)

In △ACD

AD=AC

hence, ∠ADC=∠ACD=2x (Isosceles triangle property)

Now, ∠CAE+∠BAC=180 (Linear pair)

75+∠BAC=180

∠BAC=105

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Sum of angles of triangle ABC = 180

∠BAC+∠ABC+∠ACB=180

105+x+2x=180

3x=75

x=25

Thus, ∠ACB=∠ACD=2x=2×25=50

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