Question

Question 15
If the angles of a triangle are $x$ , $y$ and ${40}^{\circ }$, and the difference between the two angles $x$ and $y$ is ${30}^{\circ }$, then , find the value of $x$ and $y$.

Answer 1

Given that, $x$, $y$ and ${40}^{\circ }$ are the angles of a triangle.
$x+y+{40}^{\circ }={180}^{\circ }$
[Since, the sum of all the angles of trangle is ${180}^{\circ }$.]
$\Rightarrow$ $x+y={140}^{\circ }$...(i)
Also,
$x–y={30}^{\circ }$...(ii)
On adding Eqs. (i) and (ii), we get
2x = ${170}^{\circ }$
$x={85}^{\circ }$
On putting x = ${85}^{\circ }$ in Eq. (i), we get
${85}^{\circ }+y={140}^{\circ }\Rightarrow y={55}^{\circ }$
Hence, the required values of $x$ and $y$ are ${85}^{\circ }and{55}^{\circ }$, respectively.