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In quadrilateral ABCD, AB = AD and BC = CD. Show that Angle ABC = Angle ADC.
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Given, AB = AD
BC = CD
AC which is common to both ∆ADC and ∆ABC.
So, ∠DAC = ∠CAB = 30 as AB = AD and AC which is common.
And, ∠DCA = ∠ACB = 50 as BC = CD and AC which is common.
Now, we know sum of all interior angles of a triangle is 180⁰.
In ∆ADC,
∠a + ∠d + ∠c = 180⁰
30⁰ + ∠d + 50⁰ = 180
80⁰ + ∠d = 180⁰
∠d = 180⁰-80⁰
∠d = 100⁰
In ∆ABC,
∠a + ∠b + ∠c = 180⁰
30⁰ + ∠b + 50⁰ = 180⁰
80⁰ + ∠b = 180⁰
∠b = 180⁰-80⁰
∠b = 100⁰
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