Mathematics
In the following figure, find the value of x:
Triangles
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Answer
△ABD is an isosceles triangle with BD = AD,
∴ ∠DBA = ∠BAD = 48°.
We know that,
An exterior angle is equal to the sum of two opposite interior angles,
Ext. ∠ADC = ∠BAD + ∠DBA = 48° + 48° = 96°.
△ADC is an isosceles triangle with AD = DC,
∴ ∠DAC = ∠DCA = x°.
Since, sum of angles of triangle = 180°.
Considering △ADC we get,
⇒ ∠DAC + ∠ADC + ∠DCA = 180°
⇒ x° + 96° + x° = 180°
⇒ 2x° + 96° = 180°
⇒ 2x° = 180° - 96° = 84°
⇒ x° = 42°
Hence, x = 42°.
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