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What is the value of $x$ in the figure shown above?
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07 Aug 2025, 23:31
07 Aug 2025, 23:31
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100% (00:33) correct
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What is the value of $x$ in the figure shown above?
(A) $\(72^{\circ}\)$
(B) $\(90^{\circ}\)$
(C) $\(105^{\circ}\)$
(D) $\(108^{\circ}\)$
(E) $\(120^{\circ}\)$
Re: What is the value of $x$ in the figure shown above?
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20 Aug 2025, 08:55
20 Aug 2025, 08:55
Expert Reply
As two angles of triangle CDE are $60^{\circ}$ each, the third angle DCE would be $\(180^{\circ}-\left(60^{\circ}+60^{\circ}\right)= 180^{\circ}-120^{\circ}=60^{\circ}\)$
Next as $B C E$ is a straight line, the sum of the angle $A C B$, angle $\(A C D\)$ \& angle $D C E$ should be 180 degrees, so we get $\(12^{\circ}+x^{\circ}+60^{\circ}=180^{\circ}\)$ which gives $\(x=180^{\circ}-\left(12^{\circ}+60^{\circ}\right)=180^{\circ}-72^{\circ}=\)$ 108 degrees.
Hence the value of angle $x$ is 108 degrees, so the answer is (D).
Next as $B C E$ is a straight line, the sum of the angle $A C B$, angle $\(A C D\)$ \& angle $D C E$ should be 180 degrees, so we get $\(12^{\circ}+x^{\circ}+60^{\circ}=180^{\circ}\)$ which gives $\(x=180^{\circ}-\left(12^{\circ}+60^{\circ}\right)=180^{\circ}-72^{\circ}=\)$ 108 degrees.
Hence the value of angle $x$ is 108 degrees, so the answer is (D).
gmatclubot
Re: What is the value of $x$ in the figure shown above? [#permalink]
20 Aug 2025, 08:55
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