Question

In the given figure $AB\parallel CD.$ Find x + y if all measurements are indicated in centimeter.

• A. 4.5 cm
• B. 7.5 cm
• C. 6.5 cm
• D. 2.75 cm

Answer 1

The correct option is B 7.5 cm

In $△CZD$ and $△BZA$

$\angle CZD=\angle BZA$ (Vertically opposite angles)

$\angle C=\angle B$ (corresponding angles)

$\angle A=\angle D$ (corresponding angles)

So, $△CZD\sim \angle BZA$ ($AAA$ criteria)

using $BPT,$

$\frac{1.8}{y}=\frac{3}{5}=\frac{2.7}{x}$

On solving, we get $x=4.5,y=3.$

So, $x+y=7.5cm.$