Question

Figure shows an equilateral triangle with two of its vertices on sides of a square and its third vertex on a vertex of the square. Calculate the value of $y-x$.

• A. $45$
• B. $60$
• C. $75$
• D. $90$
• E. It cannot be determined from the information given

Answer 1

Answer: (B)

$60$

In figure $ABCD$ is a square and $DEF$ is a equilateral triangle

Then $\angle DEF=\angle EDF=\angle EDF={60}^0$

In right angle $△DCF$

$\angle FDC+\angle DFC={90}^0\Rightarrow \angle FDC=90-y$

In Angle $ADC$

$\angle ADE+\angle EDF+\angle FDC={90}^0$

$\Rightarrow x+60+90-y=90$

$\Rightarrow y-x={60}^0$