Question

In the diagram below the lager angle is 4 times bigger than the smaller angle.find larger angle

Answer 1

Let the smaller angle be

`=x`

The larger angle is 4 times bigger than the smaller angle means

`\begin{gathered} \text{larger angle =y} \\ \text{Therefore,} \\ y=4* x \\ y=4x \end{gathered}`

Concept:

The sum of two or more angles on a straight line is always 180°

Therefore,

`x+y=180^0`

By substituting the value of y=4x in the equation above, we will have

`\begin{gathered} x+4x=180^0 \\ 5x=180^0 \\ \text{divide both sides by 5} \\ (5x)/(5)=(180^0)/(5) \\ x=36^0 \end{gathered}`

substitute the value of x= 36° in y=4x to find the value of the bigger angle

`\begin{gathered} y=4x \\ \text{when x=36} \\ y=4*36 \\ y=144^0 \end{gathered}`

Hence,

The larger angle is =144 °

OPTION D IS THE CORRECT ANSWER