Discussion
ABCD is a rhombus in which ∠ ADB = 25°. Then, the value of (2 ∠ BAD - ∠ ABC) is :
Answer: C
The value is 210°.
In a rhombus each diagonal bisects the vertex angles, so ∠ADC = 2 × 25° = 50°. Opposite angles are equal and adjacent angles are supplementary:
\[ \begin{aligned} \angle ABC &= \angle ADC = 50^\circ \\ \angle BAD &= 180^\circ - 50^\circ = 130^\circ \\ 2\angle BAD - \angle ABC &= 260^\circ - 50^\circ = 210^\circ \end{aligned} \]
260° is 2 ∠BAD before subtracting ∠ABC, and 230° and 240° come from taking ∠ABC as 30° or 20° instead of 50°.
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