Q14. - Algebra 2

Question

Four lines on a plane intersect in one point, forming 8 equal angles that are non-overlapping. What is the measure, in degrees, of one of these angles ?

Step-by-Step Solution

Answer

The measure of one of the angles formed by intersecting four lines at one point is $45$ degrees.

Step 1 – Graphical interpretation of the given data.

Four lines intersect at one point, forming 8 equal angles that are non-overlapping.

 

This can be diagrammatically shown as below:

Here, $a1,a2,a3,a4,a5,a6,a7,\text{ and }a8$are 8 equal angles.

Step 2 – Find an equation that is used to find the measure of one of the angle.

From the figure it is clear that, the sum of 8 angles is 360 degrees.

Let $x$ be the measure of the one of the 8 angles.

 

Here, measure of 8 angles is equal.

Then the sum of 8 angles equal to 360 degrees can be mathematically written as follows:

$\begin{array}{l}x+x+x+x+x+x+x+x=360\\ 8x=360\end{array}$

Step 3 – Find value of x.

Solve $8x=360$:

$\left\{\begin{array}{c}8x=360\\ x=\frac{360}{8}\\ x=45\end{array}\right\}$

Hence, The measure of one of the angles formed by intersecting four lines at one point is $45$ degrees.