Question

If the two triangles $ABC$ and $PQR$ are similar and $x:y=1:2$, then

• A. $x=22°,y=44°$
• B. $x=22°,y=88°$
• C. $x=44°,y=22°$
• D. $x=44°,y=88°$

Answer 1

Answer: (A), (C)

$x=44°,y=22°$

The given diagram is
Since, $\Delta ABC\sim \Delta PQR$
The triangle will look like

The sum of the interior angles of a triangle is ${180}^{\circ }$.

Therefore,
$x+2y+{70}^{\circ }={180}^{\circ }$

$x+2y={180}^{\circ }-{70}^{\circ }$

$x+2y={110}^{\circ }$ . . . (i)

Given: $x:y=1:2$

$\frac{x}{y}=\frac{1}{2}$

$2x=y$ . . .(ii)

Substituting equation (ii) in (i),

$x+2\left(2x\right)={110}^{\circ }$

$x+4x={110}^{\circ }$

$5x={110}^{\circ }$

$x=\frac{{110}^{\circ }}{5}$

$x={22}^{\circ }$

From equation (ii),
$2x=y$

$2\times {22}^{\circ }=y$

$y={44}^{\circ }$

Therefore, $x=22,y=44$