Question

Find the value of a and b in the given figure.




a = 100°; b = 110°

a = 90°; b = 110°

a = 110°; b = 90°

a = 95°; b = 115°

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Answer 1

Answer:

Let the given triangle be ABC such that ∠ABC=36. A line through C meets AB at D.

Now, In △DBC,

DB=DC (Given)

hence, ∠DBC=∠DCB=36

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(Isosceles triangle property)

Sum of angles of triangle = 180

∠DBC+∠DCB+∠CDB=180

36+36+∠CDB=180

∠CDB=108

Now, ∠ADC=180−∠ADB

∠ADC=180−108

∠ADC=72

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in △ADC,

∠ADC=∠DAC=72

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(Isosceles triangle property, AC= CD is given)

Sum of angles = 180

∠ADC+∠CAD+∠ACD=180

72+72+x=180

x=180−144

x=36

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