Question

3. Angles X and Y have a sum of 159 degrees. Angle X is 43 degrees smaller than angle Y.

Write a system of equations that represent this, then solve it to find the measures of both
angles.

Answer 1

`\underline{\underline{\large\bf{Solution:-}}}\\`

`\longrightarrow`Since angle X and Y have a sum of 159

`\implies \bf Y + X= 159 \_\_\_\_(1)`

`\longrightarrow`Since X is 43 degrees smaller than Y , so subtracting X from Y would give 43 , therefore equation will be written as -

`\implies \bf Y - X = 43 \_\_\_\_(2)`

Adding Equation (1) and (2)

`\begin{gathered}\\\implies\quad \sf Y+X+Y-X = 159+43 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf Y+Y + X-X = 202 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf 2Y = 202 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf Y = (202)/(2) \\\end{gathered}`

`\begin{gathered}\\\implies\quad \boxed{\sf {Y = 101 }} \\\end{gathered}`

Putting Y in eq (1)

`\begin{gathered}\\\implies\quad \sf X + 101 = 153 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf X = 153-101 \\\end{gathered}`

`\begin{gathered}\\\implies\quad \boxed{\sf{ X = 52 }}\\\end{gathered}`