Discussion
In a pentagon ABCDE, \(\angle A = (2x + 9^\circ)\), \(\angle B = (2x + 1^\circ)\), \(\angle C = (2x - 1^\circ)\), \(\angle D = (2x + 5^\circ)\) and \(\angle E = (2x - 4^\circ)\). Then, value of \((2x + 10^\circ)\) is :
Answer: C
The value of \((2x + 10^\circ)\) is 116°.
The interior angles of a pentagon add up to \((5 - 2) \times 180^\circ = 540^\circ\).
\[ \begin{aligned} 10x + (9 + 1 - 1 + 5 - 4)^\circ &= 540^\circ \\ 10x + 10^\circ &= 540^\circ \\ x &= 53^\circ \end{aligned} \]
So \(2x + 10^\circ = 106^\circ + 10^\circ = 116^\circ\). The other three values would each need a different x, and none of those makes the five angles add up to 540°.
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