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ABCD is a rhombus. 

∠DAB = 2x + 15°, 

∠DCB = 3x – 30°, 

∠BDC equals

(a) 45° 

(b) 35° 

(c) 37.5° 

(d) 42.5°

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Best answer

(c) 37.5°

∴Opp ∠s of a rhombus are equal 

2x + 15° = 3x – 30° ⇒ x = 45° 

In ΔBCD, CD = CB ⇒ ∠CBD = ∠BDC 

Also, ∠DCB= 3 × 45° – 30° = 105° 

∴ ∠BDC = \(\frac{180° - 105°}{2}=\frac{75°}{2}\) = 37.5°.

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