Question

In the given diagram , $ABC$ is a staright line
(ii) If $y=1\frac{1}{2}$ right angle ; find $x$.

Answer 1

Given, $y=1\frac{1}{2}$ right angle

$y=1\frac{1}{2}\times {90}^{\circ }$

$y=\frac{2\times 1+1}{2}\times {90}^{\circ }$

$y=\frac{3}{2}\times {90}^{\circ }$

$y={135}^{\circ }$

$\because$ $ABC$ is a straight line

$\therefore$ $\angle ABC={180}^{\circ }$


$\Rightarrow$ $\angle ABD+\angle DBC={180}^{\circ }$ [from figure]

$x+y={180}^{\circ }$

$x+{135}^{\circ }={180}^{\circ }$

$x={180}^{\circ }-{135}^{\circ }$

$\therefore$ $x={45}^{\circ }$

Hence, if $y=1\frac{1}{2}$ right angle then $x={45}^{\circ }$.