Question

A quadrilateral has two angles that measure 150° and 140°. The other two angles are in aratio of 3:4. What are the measures of those two angles?o ando

Answer 1

Let the quadrilateral be

From the above

`\begin{gathered} x+y+140+150=360 \\ x+y+290=360 \\ x+y=360-290 \\ x+y=70 \\ \text{Multiply through by 4} \\ 4x+4y=280\ldots\ldots\ldots\text{.}(1) \end{gathered}`

Without the loss of generality, let

`\begin{gathered} x\colon y=3\colon4 \\ (x)/(y)=(3)/(4) \\ \text{cross multiply} \\ 4x=3y \end{gathered}`

Substitute 4x = 3y into equation (1)

`\begin{gathered} 4x+4y=280 \\ 3y+4y=280 \\ 7y=280 \\ y=(280)/(7) \\ y=40 \end{gathered}`

From

`\begin{gathered} x+y=70 \\ x=70-y \\ x=70-40 \\ x=30 \end{gathered}`

Therefore, the two angles are

`30^(\circ),40^(\circ)`