Mathematics
In the given figure, △ABD ≅ △ACD. If ∠DAC = 30° and ∠BDC = 110°, then the measure of ∠DBA is :
30°
50°
70°
25°
Triangles
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Answer
Given,
△ABD ≅ △ACD
Since, corresponding parts of congruent triangles are equal.
⇒ ∠DBA = ∠ACD = y (let)
⇒ ∠ADB = ∠ADC = x (let)
From figure,
⇒ ∠ADB + ∠ADC + ∠BDC = 360°
⇒ x + x + 110° = 360°
⇒ 2x = 360° - 110°
⇒ 2x = 250°
⇒ x =
⇒ x = 125°
⇒ ∠ADC = 125°
In △ADC,
By angle sum property of triangle,
⇒ ∠ADC + ∠ACD + ∠CAD = 180°
⇒ 125° + y + 30° = 180°
⇒ 155° + y = 180°
⇒ y = 180° - 155°
⇒ y = 25°
⇒ ∠DBA = y = 25°.
Hence, option 4 is the correct option.
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Related Questions
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Reason (R): Sum of two sides of a triangle is greater than the third side.
A is true, R is false
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Both A and R are true
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