Question

In the given diagram, \(ABC\) is a straight line.
ii If \(y=1\dfrac{1}{2}\) right angles; find \(x\).

Answer 1

Given: \(y=1\dfrac{1}{2}\)right angle
\(y=1\dfrac{1}{2}\times 90^{\circ}\)
\(y = \dfrac{2\times 1+1}{2}\times 90^{\circ}\)
\(y=\dfrac{3}{2}\times 90^{\circ}\)
\(y=135^{\circ}\)
\(\because ABC\) is 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 \(y=1\dfrac{1}{2}\)right angle then \(x=45^{\circ}\).