Question

In the given figure, if AD || BC then find the value of y - x.

• A. ${20}^{\circ }$
• B. ${25}^{\circ }$
• C. ${30}^{\circ }$
• D. ${35}^{\circ }$

Answer 1

The correct option is A ${20}^{\circ }$

It is given that AD || BC, hence CD is a transversal

∠BCD = ∠EDC [alternate interior angles]
$\Rightarrow (x+25{)}^{\circ }={60}^{\circ }$
$\Rightarrow x={60}^{\circ }-{25}^{\circ }$
$\Rightarrow x={35}^{\circ }$

Using the angle sum property for triangle ABC
$\Rightarrow x+y+{90}^{\circ }={180}^{\circ }$
$\Rightarrow {35}^{\circ }+y+{90}^{\circ }={180}^{\circ }$
$\Rightarrow y+{125}^{\circ }={180}^{\circ }$
$\Rightarrow y={180}^{\circ }-{125}^{\circ }$
$\Rightarrow y={55}^{\circ }$

The value of y - x is ${55}^{\circ }-{35}^{\circ }$
$\Rightarrow {20}^{\circ }$