Question

The angles in a rectangle are given by $(x+30{)}^{\circ }$ and $(y+50{)}^{\circ }$ respectively. What other information is required to find the value of $x+y$ ?

• A. We need the value of $x$ so that we can find one angle and then find $y$ using the value of $x$
• B. We need the value of $y$ so that we can find one angle and then find $x$ using the value of $y$
• C. No extra information is necessary and $x+y={90}^{\circ }$
• D. No extra information is necessary and $x+y={100}^{\circ }$

Answer 1

The correct option is D No extra information is necessary and $x+y={100}^{\circ }$

We know that in a rectangle, all angles are equal to ${90}^{\circ }$.
So, the angles $(x+30{)}^{\circ }$ and $(y+50{)}^{\circ }$ need to be equated to ${90}^{\circ }$ respectively. This gives us the following equations:

$(x+30{)}^{\circ }={90}^{\circ }$ and
$(y+50{)}^{\circ }={90}^{\circ }$

Solving these equations, we get $x={60}^{\circ }$ and $y={40}^{\circ }$ respectively and therefore, $x+y={100}^{\circ }$.