Mathematics
In the following figure, find the value of x:
Triangles
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Answer
From figure,
∠ACD = 180° - 130° = 50°.
In △ADC, AD = CD.
∴ ∠DAC = ∠ACD = 50°.
∠ADC = 180° - (∠CAD + ∠DCA) = 180° - (50° + 50°) = 80°.
From figure,
∠ADB + ∠ADC = 180°
∠ADB = 180° - ∠ADC = 180° - 80° = 100°.
In △ADB,
∠DBA = ∠DAB = x° (As angles opposite to equal sides are equal)
∠DBA + ∠DAB + ∠ADB = 180°
x° + x° + 100° = 180°
2x° = 80°
x° = 40°
Hence, x = 40°.
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