Question

In the given figure, CD $\perp$ AC, CD $\parallel$ AE,
$\angle$ ADE = 28${}^o$ and $\angle$ DEB = 85${}^o$. Find the values of x and y.

• A. $x={57}^o\text{and}y={33}^o$
• B. $x={33}^o\text{and}y={57}^o$
• C. $x={57}^o\text{and}y={28}^o$
• D. $x={90}^o\text{and}y={33}^o$

Answer 1

The correct option is A $x={57}^o\text{and}y={33}^o$

Given, CD $\parallel$ AE
$\angle$ DEB = $\angle$ CDE [Alternate interior angles]
$\Rightarrow {85}^o=x+{28}^0$
$\Rightarrow x={57}^o$
$\because$ Sum o angles in a triangle is 180${}^0$
$\therefore \angle DAC+\angle ACD+\angle ADC={180}^o\Rightarrow x+y+{90}^o={180}^o\Rightarrow {57}^o+y+{90}^o={180}^o\Rightarrow y={33}^o$
CD $\perp$ AC,
$\angle$ ADE = 28${}^o$ and $\angle$ DEB = 85${}^o$