Question

In the adjoining figure $PQ\parallel XY$, also $y:z=4:5$, then $\angle X$=

• A. ${100}^o$
• B. ${80}^o$
• C. ${120}^o$
• D. ${110}^o$

Answer 1

The correct option is A ${100}^o$

Given that

$PQ||XY$

$y:z=4:5,\angle x=?$

let the ratio = x

then $y=4x$

$z=5x$

so, $\angle x=\angle z$ (After note angle)

$\angle x=\angle z=\angle m$ (After note angle)

But

$\angle x+\angle y={180}^o$

$\angle z+\angle y={180}^o$

$4x+5x={180}^o$

$9x={180}^o$

$x={20}^o$

then, $y=4x=4\times {20}^o={80}^o$

$y={80}^o$

$z=5x=5\times {20}^o={100}^o$